OpenLLM-France/wikimedia huggingface dataset:
# Literature/1931/Goldberg

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Wikimedia
### w: Emanuel Goldberg

* Goldberg and his former teacher and collaborator Robert Luther were instrumental in the acceptance at the International Congress of Photography in Dresden in 1931 of the widely adopted German national film speed DIN 4512. At the same Congress Goldberg introduced his "Statistical Machine," a document search engine that used photoelectric cells and pattern recognition to search the metadata on rolls of microfilmed documents (US patent 1,838,389, 29 December 1931). This technology was used in a variant form in 1938 by Vannevar Bush in his "microfilm rapid selector," his "comparator" (for cryptanalysis), and was the technological basis for the imaginary Memex in Bush's influential 1945 essay " As We May Think."
| w: Vannevar Bush w: Memex | w: Engineering Research Associates w: Ralph R. Shaw (librarian) |

## Chronology

* Buckland, Michael (1992). "Emanuel Goldberg, Electronic Document Retrieval, and Vannevar Bush's Memex." Journal of the American Society for Information Science, vol. 43, no. 4 (May 1992), pp. 284-294. $^{[^]}$
* Literature/1971/Kaprelian $^{[^]}$
* Literature/1961/Bagg $^{[^]}$
* Literature/1958/Fairthorne $^{[^]}$
* Literature/1957/Neumann $^{[^]}$
* Shaw, Ralph R. (1949). "Machines and the Bibliographical Problems of the Twentieth Century." (pp. 37-71) In: L. N. Ridenour, et al. Bibliography in an Age of Science. Urbana: University of Illinois Press. $^{[^]}$
* Bush, Vannevar (1945). "As We May Think." The Atlantic Monthly (July 1945): 101-108. $^{[^]}$
* Literature/1940/Schwegmann $^{[^]}$
* Literature/1939/Bush $^{[^]}$
* Bernal, J. D. (1939). The Social Function of Science. London: Routledge & Kegan Paul Ltd. $^{[^]}$
* Wells, H. G. (1938). World Brain. Garden City, NY: Doubleday, Doran & Co. $^{[^]}$
* Literature/1937/Schuermeyer $^{[^]}$
* Wells, H. G. (1936). World Encyclopaedia. Lecture delivered at the Royal Institution of Great Britain, November 20th, 1936. $^{[^]}$
* Literature/1935/Davis $^{[^]}$
* Literature/1934/Otlet $^{[^]}$
* Literature/1933/Keegstra $^{[^]}$
* Literature/1933/Schuermeyer $^{[^]}$
* Literature/1932/Sebille $^{[^]}$
* Goldberg, Emanuel (1932). "Methods of Photographic Registration." British Journal of Photography, 79: 533-534. $^{[^]}$
* Goldberg, Emanuel (1931). Statistical Machine. U.S. patent 1,838,389. Dec. 29, 1931. $^{[^]}$
# Literature/1931/Russell

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## 2nd edition
### Preface

    By David Papineau

## Wikimedia
### w: Bertrand Russell

| w: Scientific method | w: Philosophy of science |

## Chronology

* Wells, H. G. (1938). World Brain. Garden City, NY: Doubleday, Doran & Co. $^{[^]}$
* Wells, H. G. (1933). The Shape of Things to Come. Hutchinson. $^{[^]}$
* Russell, Bertrand (1931). The Scientific Outlook. London: George Allen & Unwin. $^{[^]}$
* Russell, Bertrand (1926). "The Meaning of Meaning." Dial, vol.81 (August 1926) pp. 114-121. $^{[^]}$
* Ogden, C. K. & I. A. Richards (1923). The Meaning of Meaning: A Study of the Influence of Language upon Thought and of the Science of Symbolism. London: Routledge & Kegan Paul Ltd. $^{[^]}$
* Wells, H. G. (1923). Men Like Gods. Cassell and Co., Ltd. $^{[^]}$
* Wittgenstein, Ludwig (1922). Tractatus Logico-Philosophicus. Frank P. Ramsey & C. K. Ogden, trans., Kegan Paul, 1922. $^{[^]}$
* Russell, Bertrand (1921). The Analysis of Mind. London: George Allen & Unwin. $^{[^]}$
* Watson, John B. (1913). "Psychology as the behaviorist views it," Psychological Review, 20, pp. 158-177. $^{[^]}$
* Russell, Bertrand (1905). "On Denoting." Mind, vol. 14, pp. 479-493. $^{[^]}$
* Wells, H. G. (1905). A Modern Utopia. New York, NY: Penguin Group, 2005. $^{[^]}$
* Pavlov, Ivan (1903). "The Experimental Psychology and Psychopathology of Animals." The 14th International Medical Congress, Madrid, Spain, April 23-30, 1903. $^{[^]}$
# Literature/1929

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Subpages

* Literature/1929/Cassirer $^{[^]}$
* Literature/1929/Huxley $^{[^]}$
* Literature/1929/Lewis $^{[^]}$
* Literature/1929/Richards $^{[^]}$
* Literature/1929/Whitehead $^{[^]}$
# Literature/1932

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Subpages

* Literature/1932/Cassirer $^{[^]}$
* Huxley, Aldous (1932). Brave New World. Harper Perennial, 1932. $^{[^]}$
# Literature/1930/Empson

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Wikimedia
### w: Seven Types of Ambiguity

* The first type of ambiguity is the metaphor, that is, when two things are said to be alike which have different properties. This concept is similar to that of metaphysical conceit.
* Two or more meanings are resolved into one. Empson characterizes this as using two different metaphors at once.
* Two ideas that are connected through context can be given in one word simultaneously.
* Two or more meanings that do not agree but combine to make clear a complicated state of mind in the author.
* When the author discovers his idea in the act of writing. Empson describes a simile that lies halfway between two statements made by the author.
* When a statement says nothing and the readers are forced to invent a statement of their own, most likely in conflict with that of the author.
* Two words that within context are opposites that expose a fundamental division in the author's mind.
| w: Ambiguity | w: Implicature |

## Chronology

* Richards, I. A. (1936). The Philosophy of Rhetoric. Oxford University Press. $^{[^]}$
* Korzybski, Alfred (1933). Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics. 5th ed., Institute of General Semantics, 1994. $^{[^]}$
* Magritte, René (1933). The Human Condition (La condition humaine). National Gallery of Art, Washington DC. $^{[^]}$
* Wells, H. G. (1933). The Shape of Things to Come. Hutchinson. $^{[^]}$
* Empson, William (1930). Seven Types of Ambiguity, 2nd ed., London: Chatto & Windus, 1949. $^{[^]}$
* Magritte, René (1929). The Treachery of Images (La trahison des images). Los Angeles County Museum of Art, Los Angeles, California. $^{[^]}$
* Ogden, C. K. & I. A. Richards (1923). The Meaning of Meaning: A Study of the Influence of Language upon Thought and of the Science of Symbolism. London: Routledge & Kegan Paul Ltd. $^{[^]}$
# Literature/1930/Frank

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Wikimedia
### w: Jerome Frank

| w: Legal realism | w: Interpretivism (legal) w: Interpretivism (sociology) |

## Chronology

* Literature/1977/Dworkin $^{[^]}$
* Skinner, B. F. (1957). Verbal Behavior. Acton, Massachusetts: Copley Publishing Group. $^{[^]}$
* Austin, J. L. (1955). How to Do Things with Words. The William James Lectures delivered at Harvard University in 1955, ed. by J. O. Urmson. Oxford: Clarendon, 1962. $^{[^]}$
* Hayakawa, S. I. (1949). Language in Thought and Action. Harcourt, Brace & Company, 1949. $^{[^]}$
* Korzybski, Alfred (1933). Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics. 5th ed., Institute of General Semantics, 1994. $^{[^]}$
* Magritte, René (1933). The Human Condition (La condition humaine). National Gallery of Art, Washington DC. $^{[^]}$
* Wells, H. G. (1933). The Shape of Things to Come. Hutchinson. $^{[^]}$
* Empson, William (1930). Seven Types of Ambiguity, 2nd ed., London: Chatto & Windus, 1949. $^{[^]}$
* Frank, Jerome (1930). Law and the Modern Mind. Peter Smith, 1930. $^{[^]}$
* Magritte, René (1929). The Treachery of Images (La trahison des images). Los Angeles County Museum of Art, Los Angeles, California. $^{[^]}$
* Malinowski, Bronislaw (1923). "The Problem of Meaning in Primitive Languages." Supplement to: Ogden & Richards (1923), pp. 296-336. $^{[^]}$
* Ogden, C. K. & I. A. Richards (1923). The Meaning of Meaning: A Study of the Influence of Language upon Thought and of the Science of Symbolism. London: Routledge & Kegan Paul Ltd. $^{[^]}$
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Determinant/Zero, linear dependent and rank property/Fact/Factreferencenumber

Theorem 26.11
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Differentiable function/D in R/Chain rule/Fact/Factreferencenumber

Theorem 14.8
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Differentiable function/D in R/Linear approximation/Fact/Factreferencenumber

Theorem 14.5
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Differentiable function/D in R/Inverse function/Fact/Factreferencenumber

Theorem 14.9
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Diagonal matrix/Eigenvalues/Example/Examplereferencenumber

Example 27.7
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Differentiable function/D in R/Continuity in point/Fact/Factreferencenumber

Corollary 14.6
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Differentiable function/D in R/Rules/Fact/Factreferencenumber

Lemma 14.7
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Determinant/Recursively/Alternating/Swap property/Fact/Factreferencenumber

Theorem 26.10
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Determinant/Recursively/Multilinear/Fact/Factreferencenumber

Theorem 26.9
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Determinant/Transposed matrix/Universal property/Fact/Factreferencenumber

Theorem 26.15
# Literature/1952/Hutchins

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Authors
### w: Robert Hutchins

* President (1929-1945) and Chancellor (1945-1951), University of Chicago

## Wikimedia
### w: Great Books of the Western World

* Hutchins said "This is more than a set of books, and more than a liberal education. Great Books of the Western World is an act of piety. Here are the sources of our being. Here is our heritage. This is the West. This is its meaning for mankind."
* In his Europe: A History, Norman Davies criticizes the compilation for overrepresenting selected parts of the western world, especially Britain and the U.S., while ignoring the other, particularly Central and Eastern Europe. According to his calculation, in 151 authors included in both editions, there are 49 English or American authors, 27 Frenchmen, 20 Germans, 15 ancient Greeks, 9 ancient Romans, 6 Russians, 4 Scandinavians, 3 Spaniards, 3 Italians, 3 Irishmen, 3 Scots, and 3 Eastern Europeans. Prejudices and preferences, he concludes, are self-evident.
| w: Great Books w: Western canon w: Western thought | w: Encyclopaedia Britannica w: World Encyclopedia |

## Chronology

* Literature/1990/Adler $^{[^]}$
* Adler, Mortimer J. & Geraldine van Doren (1988). Reforming Education: The Opening of the American Mind. New York: Macmillan. $^{[^]}$
* Bloom, Allan (1987). The Closing of the American Mind: How Higher Education Has Failed Democracy and Impoverished the Souls of Today's Students. New York: Simon & Schuster. $^{[^]}$
* Adler, Mortimer J. & Paideia Group (1982). The Paideia Proposal: An Educational Manifesto. New York: Simon & Schuster. $^{[^]}$
* Hall, Edward (1976). Beyond Culture. New York: Doubleday. $^{[^]}$
* Feyerabend, Paul (1975). Against Method: Outline of an Anarchist Theory of Knowledge. New Left Books. $^{[^]}$
* Pirsig, Robert (1974). Zen and the Art of Motorcycle Maintenance: An Inquiry into Values. William Morrow & Co. $^{[^]}$
* Geertz, Clifford (1973). The Interpretation of Cultures: Selected Essays. New York: Basic Books. $^{[^]}$
* Hutchins, Robert, ed. (1952). Great Books of the Western World. Encyclopaedia Britannica. $^{[^]}$
* Wells, H. G. (1938). World Brain. Garden City, NY: Doubleday, Doran & Co. $^{[^]}$
# Literature/1953/Skinner

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Abridgements

* Peter A. Morton. A Historical Introduction to the Philosphy of Mind: Readings With Commentary, 2nd ed. Broadview Press, 2010.

## Wikimedia
### w: B. F. Skinner

| w: Verbal Behavior | w: Beyond Freedom and Dignity w: Walden Two |

## Chronology

* Literature/1976/Skinner $^{[^]}$
* Skinner, B. F. (1971). Beyond Freedom and Dignity. Alfred A Knopf, 1971. $^{[^]}$
* Literature/1963/Gabor $^{[^]}$
* Chomsky, Noam (1959). "A Review of B. F. Skinner's Verbal Behavior." Language, 35(1): 26-57. $^{[^]}$
* Skinner, B. F. (1957). Verbal Behavior. Acton, Massachusetts: Copley Publishing Group. $^{[^]}$
* Skinner, B. F. (1953). Science and Human Behavior. Macmillan Co., 1948. $^{[^]}$
* Orwell, George (1949). Nineteen Eighty-Four. London: Secker and Warburg, 1949. $^{[^]}$
* Skinner, B. F. (1948). Walden Two. Macmillan Co., 1948. $^{[^]}$
* Orwell, George (1945). Animal Farm: A Fairy Story. London: Secker and Warburg, 1945. $^{[^]}$
* Literature/1945/Popper $^{[^]}$
* Wells, H. G. (1938). World Brain. Garden City, NY: Doubleday, Doran & Co. $^{[^]}$
* Wells, H. G. (1933). The Shape of Things to Come. Hutchinson. $^{[^]}$
* Huxley, Aldous (1932). Brave New World. Harper Perennial, 1932. $^{[^]}$
* Russell, Bertrand (1926). "The Meaning of Meaning." Dial, vol.81 (August 1926) pp. 114-121. $^{[^]}$
* Ogden, C. K. & I. A. Richards (1923). The Meaning of Meaning: A Study of the Influence of Language upon Thought and of the Science of Symbolism. London: Routledge & Kegan Paul Ltd. $^{[^]}$
* Wells, H. G. (1923). Men Like Gods. Cassell and Co., Ltd. $^{[^]}$
* Russell, Bertrand (1921). The Analysis of Mind. London: George Allen & Unwin. $^{[^]}$
* Watson, John B. (1913). "Psychology as the behaviorist views it," Psychological Review, 20, pp. 158-177. $^{[^]}$
* Wells, H. G. (1905). A Modern Utopia. New York, NY: Penguin Group, 2005. $^{[^]}$
* Pavlov, Ivan (1903). "The Experimental Psychology and Psychopathology of Animals." The 14th International Medical Congress, Madrid, Spain, April 23-30, 1903. $^{[^]}$
# Literature/1954

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Subpages

* Black, Max (1954). "Metaphor." Proceedings of the Aristotelian Society, 55, pp. 273-294. $^{[^]}$
* Literature/1954/Tolkien $^{[^]}$
# Literature/1952

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Subpages

* Literature/1952/Ashby $^{[^]}$
* Literature/1952/Egan $^{[^]}$
* Literature/1952/Hare $^{[^]}$
* Literature/1952/Hodgkin $^{[^]}$
* Hutchins, Robert, ed. (1952). Great Books of the Western World. Encyclopaedia Britannica. $^{[^]}$
# Literature/1954/Black

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Wikimedia

| w: Metaphor w: Implicature w: Entailment w: Presupposition | w: Ambiguity w: Pragmatics |

## Chronology

* Lakoff, George & Mark Johnson (1980). Metaphors We Live By. University of Chicago Press. $^{[^]}$
* Black, Max (1979). "More about Metaphor." In: Ortony, Andrew, ed. (1979). Metaphor and Thought, Cambridge University Press. 2nd. ed. 1993. $^{[^]}$
* Ricoeur, Paul (1975). The Rule of Metaphor: Multi-Disciplinary Studies in the Creation of Meaning in Language. Robert Czerny, Kathleen McLaughlin & John Costello, trans., London: Routledge and Kegan Paul, 1978. $^{[^]}$
* Black, Max (1962). Models and Metaphors: Studies in Language and Philosophy. Cornell University Press.
* Black, Max (1954). "Metaphor." Proceedings of the Aristotelian Society, 55, pp. 273-294. $^{[^]}$
* Black, Max (1937). "Vagueness: An exercise in logical analysis". Philosophy of Science 4: 427-455. Reprinted in: R. Keefe & P. Smith, eds., Vagueness: A Reader, MIT Press, 1997.
* Huxley, Aldous (1940). Words and Their Meanings. The Ward Ritchie Press, 1940. $^{[^]}$
* Richards, I. A. (1936). The Philosophy of Rhetoric. Oxford University Press. $^{[^]}$
* Empson, William (1930). Seven Types of Ambiguity, 2nd ed., London: Chatto & Windus, 1949. $^{[^]}$
* Ogden, C. K. & I. A. Richards (1923). The Meaning of Meaning: A Study of the Influence of Language upon Thought and of the Science of Symbolism. London: Routledge & Kegan Paul Ltd. $^{[^]}$
# Literature/1953

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Subpages

* Literature/1953/Berlin $^{[^]}$
* Literature/1953/Carnap $^{[^]}$
* Literature/1953/Harsanyi $^{[^]}$
* Wittgenstein, Ludwig (1953). Philosophical Investigations. Blackwell Publishing. $^{[^]}$
# Literature/1954/Gowers

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Revisions

* Plain Words (1948) at the request of Sir w: Edward Bridges (then head of the Civil Service)
* The ABC of Plain Words (1951)
* The Complete Plain Words (1954)
** rev. Bruce Fraser (1973)
** rev. Sidney Greenbaum & Janet Whitcut (1986)

## Excerpts

* The purpose of this book is to help officials in their use of written English as a tool of their trade. (1958)

## Wikimedia

| w: Plain English w: Plain English Campaign w: Simple English Wikipedia w: Simplified English for technical purposes w: Anglish w: Scribes: The American Society of Legal Writers | w: Politics and the English Language w: Basic English w: Universal language w: World Brain |

## Chronology

* Wittgenstein, Ludwig (1953). Philosophical Investigations. Blackwell Publishing. $^{[^]}$
* Hayakawa, S. I. (1949). Language in Thought and Action. Harcourt, Brace & Company, 1949. $^{[^]}$
* Gowers, Ernest (1948). Plain Words.
* Orwell, George (1946). "Politics and the English Language." Horizon, vol. 13, no. 76 (April), 252-265. $^{[^]}$
* Huxley, Aldous (1940). Words and Their Meanings. The Ward Ritchie Press, 1940. $^{[^]}$
* Bernal, J. D. (1939). The Social Function of Science. London: Routledge & Kegan Paul Ltd. $^{[^]}$
* Wells, H. G. (1938). World Brain. Garden City, NY: Doubleday, Doran & Co. $^{[^]}$
* Richards, I. A. (1936). The Philosophy of Rhetoric. Oxford University Press. $^{[^]}$
* Korzybski, Alfred (1933). Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics. 5th ed., Institute of General Semantics, 1994. $^{[^]}$
* Ogden, C. K. (1930). Basic English: A General Introduction with Rules and Grammar. London: Paul Treber. $^{[^]}$
* Ogden, C. K. & I. A. Richards (1923). The Meaning of Meaning: A Study of the Influence of Language upon Thought and of the Science of Symbolism. London: Routledge & Kegan Paul Ltd. $^{[^]}$
* Welby, Victoria Lady (1911). Significs and Language: The Articulate Form of Our Expressive and Interpretive Resources. H. Walter Schmitz, ed., John Benjamins, 1985. $^{[^]}$
# Literature/1951

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Subpages

* Literature/1951/Fast $^{[^]}$
* Literature/1951/Lewin $^{[^]}$
* Literature/1951/Piaget $^{[^]}$
* Literature/1951/Rogers $^{[^]}$
# Northern Arizona University/Environmental Ethics/Journals/Fall 2010 journals

* McWane F.'s Journal
* Selina's Journal
* Reid's Journal
# Northern Arizona University/Environmental Ethics/Journals/Jeff Downard's journal

My aim in this first set of entries is to reconstruct Leopold's argument in "The Land Ethic". As I work through the parts of the argument, I will attempt to identify the key philosophical ideas and questions that are both explicitly and implicitly at play in the argument.
The first thing I note is that Leopold is making a historical comparison between the ethical values that helped to guide the lives of Greek citizens at the time of Homer and the ethical values that help to guide our lives in 21st century America. The comparison is interesting both for the dramatic differences between these two worlds, as well as the remarkably similarities between the kinds of lives that people lived then and the ones we are living now.
Leopold's first main claim is that over the course of centuries, there have been significant changes in these values.
# Northern Arizona University/Environmental Ethics/Journals/Jonathan B's Journal

Jonathan Barlow PHI 331 (September 2nd, 2010)
Perhaps my first entry is too fragmented, I wrote this one in very much of a free-form writing style.
Journal Entry #1
“One must imagine Sisyphus happy.” This is what Camus tells us.
The land Ethic is nothing new to me, having read it before, I find myself once again reaffirming past ideas and truths. Of course, we must treat the natural world around us as we treat our human neighbors. Its not property of someone, even though the fences and walls and no trespassing signs will have you think otherwise. I remind myself, daily, that we are part of nature, no matter what these four concrete walls around me imply. Our nicely squared off buildings, our right angles, and straight lines are monuments against the natural world. The built environment is trash.
Although, myself included, we all rely on this separation. Whether it is my apartment, my car, or a tent, we put a veil between ourselves and the wilderness. This reminds me of a story. Its as when Edward Abbey throws an empty beer can out his car window while driving down a desert road. Faced with this hypocritical act, he affirms that it’s the road that shouldn’t be there. If there was no road, than there would be no opportunity to litter. We’re all hypocrites.
I ponder on a question posed to the class by the Professor – between a rabbit and a child, which do you save? For many this is easily answered. “Save the child”, of course, says the Professor and the class echoes this sentiment. Yet is it really that simple? Is that not a selfish thought? I try to think in terms of equality – both are animals, both living, breathing creatures. In terms of the environment is the right choice not the rabbit? A rabbit won’t grow up to consume and destroy its surrounding world. To exhaust the natural resources of the world is a human element. To live and die with as little impact as possible. I would save the child; the instinct of kinship is too strong in me. The scales of life are still tilted and the pyramid is still very much tiered. We’re all still hypocrites. The rabbit is not our brother or sister. It is a distant cousin, easily disregarded. Easily. Without second thought – for most of us. Is this right? Is there even an answer to this conundrum? Is Sisyphus, rolling that boulder up that mountain for eternity, really happy?
# Northern Arizona University/Environmental Ethics/Journals/Leopold

Journal Entry #1 9/6/2010
Journal Entry #2
Journal Entry #3
# Matrix/11/-11/No real eigenvalue/Complex eigenvalues/Exercise

Consider the matrix
    $M={\begin{pmatrix}1&1\\-1&1\end{pmatrix}}\,.$
Show that $M$, as a real matrix, has no eigenvalue. Determine the eigenvalues and the eigenspaces of $M$ as a complex matrix.
# Matrices/2x2/Determinant 0/No subspace/Exercise

Let $D$ be the set of all real $2\times 2$-matrices
    ${\begin{pmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{pmatrix}},$
which fulfill the condition
    $a_{11}a_{22}-a_{21}a_{12}=0\,.$
Show that $D$ is not a linear subspace in the space of all $2\times 2$-matrices.
# Matrix/-4-1-23 6771 003-2 0062/Trigonalizable/Exercise

Determine, whether the real matrix
    ${\begin{pmatrix}-4&-1&-2&3\\6&7&7&1\\0&0&3&-2\\0&0&6&2\end{pmatrix}}$
is trigonalizable or not.
# Matrices/Zero divisor pair/Exercise

Compute the matrix product
    ${\begin{pmatrix}0&1\\0&0\end{pmatrix}}\cdot {\begin{pmatrix}1&0\\0&0\end{pmatrix}}.$
# Matrix/0110/Q/Diagonalizable/Exercise

Show that the matrix
    ${\begin{pmatrix}0&1\\1&0\end{pmatrix}}$
is diagonalizable over $\mathbb {Q}$.