Please answer the following question: Information: - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation. Some quantities are such by their inner nature (as number), while others are functioning as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little. A small quantity is sometimes referred to as a quantulum. - A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories, intensional definitions (which try to give the essence of a term) and extensional definitions (which proceed by listing the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions. - Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework. - In mathematics, and in particular linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose is its negation; that is, it satisfies the condition If the entry in the and is "a", i.e. then the skew symmetric condition is For example, the following matrix is skew-symmetric: - In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal, that is it switches the row and column indices of the matrix by producing another matrix denoted as A (also written A, A, A or A). It is achieved by any one of the following equivalent actions: - In mathematics , a Hamiltonian matrix is a 2n - by - 2n matrix A such that JA is symmetric , where J is the skew - symmetric matrix J = \ begin ( bmatrix ) 0 & I_n \ \ - I_n & 0 \ \ \ end ( bmatrix ) and In is the n - by - n identity matrix . In other words , A is Hamiltonian if and only if ( JA ) T = JA where ( ) T denotes the transpose . - Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces. - In mathematics, a square matrix is a matrix with the same number of rows and columns. An "n"-by-"n" matrix is known as a square matrix of order "n". Any two square matrices of the same order can be added and multiplied. What is the relationship between 'hamiltonian matrix' and 'square matrix'?
Answer:
subclass of