OpenLLM-France/wikimedia huggingface dataset:
# 200 023 002/Jordan normal form/Example

We consider the matrix
    $M={\begin{pmatrix}2&0&0\\0&2&3\\0&0&2\end{pmatrix}}\,$
and want to bring it to Jordan normal form. The vectors $u=e_{1}={\begin{pmatrix}1\\0\\0\end{pmatrix}}$ and $v=e_{2}={\begin{pmatrix}0\\1\\0\end{pmatrix}}$ are linearly independent eigenvectors to the eigenvalue $2$. We have
    $A:=M-2E_{3}={\begin{pmatrix}0&0&0\\0&0&3\\0&0&0\end{pmatrix}}\,,$
so that $u$ and $v$ span this eigenspace. An eigenvector must be the image of some vector under the matrix $A$. In fact, the linear system
    $e_{2}=Aw\,$
has the solution $w={\begin{pmatrix}0\\0\\{\frac {1}{3}}\end{pmatrix}}$. Therefore, the matrix $M$ acts in the following way
    $Mu=2u,\,Mv=2v,\,Mw=2w+v.$
Hence, the mapping is described, with respect to the basis $u,v,w$, by the matrix
    ${\begin{pmatrix}2&0&0\\0&2&1\\0&0&2\end{pmatrix}}.$
This matrix is in Jordan normal form with the Jordan blocks ${\begin{pmatrix}2\end{pmatrix}}$ and ${\begin{pmatrix}2&1\\0&2\end{pmatrix}}$.
# Upper triangular matrix/44/Jordan normal form/Example

We consider the matrix
    $M={\begin{pmatrix}3&1&0&4\\0&-1&2&1\\0&0&-1&0\\0&0&0&3\end{pmatrix}}\,$
and want to bring in in Jordan normal for. Here, we have two eigenvalues and, therefore, two two-dimensional generalized eigenspaces, which we treat separately. We have
    $M-3E_{4}={\begin{pmatrix}0&1&0&4\\0&-4&2&1\\0&0&-4&0\\0&0&0&0\end{pmatrix}}\,,$
therefore, ${\begin{pmatrix}1\\0\\0\\0\end{pmatrix}}$ belongs to the kernel. The determinant of the upper right submatrix is not $0$, so the rank of the matrix is $3$, and its kernel is one-dimensional. The second power is
    ${\begin{aligned}{\begin{pmatrix}0&1&0&4\\0&-4&2&1\\0&0&-4&0\\0&0&0&0\end{pmatrix}}^{2}&={\begin{pmatrix}0&1&0&4\\0&-4&2&1\\0&0&-4&0\\0&0&0&0\end{pmatrix}}{\begin{pmatrix}0&1&0&4\\0&-4&2&1\\0&0&-4&0\\0&0&0&0\end{pmatrix}}\\&={\begin{pmatrix}0&-4&2&1\\0&16&-16&-4\\0&0&16&0\\0&0&0&0\end{pmatrix}},\end{aligned}}$
a new element of the kernel is ${\begin{pmatrix}0\\1\\0\\4\end{pmatrix}}$. Thus, we have
    $\operatorname {GeEig} _{3}(M)=\langle {\begin{pmatrix}1\\0\\0\\0\end{pmatrix}},\,{\begin{pmatrix}0\\1\\0\\4\end{pmatrix}}\rangle \,.$
Because of
    ${\begin{pmatrix}0&1&0&4\\0&-4&2&1\\0&0&-4&0\\0&0&0&0\end{pmatrix}}{\begin{pmatrix}0\\1\\0\\4\end{pmatrix}}={\begin{pmatrix}17\\0\\0\\0\end{pmatrix}}\,,$
we can use the vectors ${\begin{pmatrix}17\\0\\0\\0\end{pmatrix}}$ and ${\begin{pmatrix}0\\1\\0\\4\end{pmatrix}}$ to establish the first Jordan block.
We have
    $M+1E_{4}={\begin{pmatrix}4&1&0&4\\0&0&2&1\\0&0&0&0\\0&0&0&4\end{pmatrix}}\,,$
therefore, ${\begin{pmatrix}1\\-4\\0\\0\end{pmatrix}}$ belongs to the kernel. The rank of this matrix is again $3$, and the kernel has dimension one. The second power is
    ${\begin{aligned}{\begin{pmatrix}4&1&0&4\\0&0&2&1\\0&0&0&0\\0&0&0&4\end{pmatrix}}^{2}&={\begin{pmatrix}4&1&0&4\\0&0&2&1\\0&0&0&0\\0&0&0&4\end{pmatrix}}{\begin{pmatrix}4&1&0&4\\0&0&2&1\\0&0&0&0\\0&0&0&4\end{pmatrix}}\\&={\begin{pmatrix}16&4&2&33\\0&0&0&4\\0&0&0&0\\0&0&0&16\end{pmatrix}},\end{aligned}}$
a new element in the kernel is ${\begin{pmatrix}0\\1\\-2\\0\end{pmatrix}}$. Thus, we have
    $\operatorname {GeEig} _{-1}(M)=\langle {\begin{pmatrix}1\\-4\\0\\0\end{pmatrix}},\,{\begin{pmatrix}0\\1\\-2\\0\end{pmatrix}}\rangle \,.$
Because of
    ${\begin{pmatrix}4&1&0&4\\0&0&2&1\\0&0&0&0\\0&0&0&4\end{pmatrix}}{\begin{pmatrix}0\\1\\-2\\0\end{pmatrix}}={\begin{pmatrix}1\\-4\\0\\0\end{pmatrix}}\,,$
we can use the vectors ${\begin{pmatrix}1\\-4\\0\\0\end{pmatrix}}$ and ${\begin{pmatrix}0\\1\\-2\\0\end{pmatrix}}$ to establish the second Jordan block. Altogether, the linear mapping defined by $M$ has, with respect the basis
    ${\begin{pmatrix}17\\0\\0\\0\end{pmatrix}}\,,{\begin{pmatrix}0\\1\\0\\4\end{pmatrix}}\,,{\begin{pmatrix}1\\-4\\0\\0\end{pmatrix}}\,,{\begin{pmatrix}0\\1\\-2\\0\end{pmatrix}},$
the Jordan normal form
    ${\begin{pmatrix}3&1&0&0\\0&3&0&0\\0&0&-1&1\\0&0&0&-1\end{pmatrix}}.$
# Polynomial ring/Field/Lemma of Bezout/Fact

Let $K$ be a field and let $P_{1},\ldots ,P_{n}$ denote polynomials over $K$. Let $G$ be a greatest common divisor of the $P_{i}$.
    $G=Q_{1}P_{1}+\cdots +Q_{n}P_{n}\,$
with
$Q_{1},\ldots ,Q_{n}\in K[X]$
# Polynomial ring/Field/Lemma of Bezout/Fact/Proof

We consider the set of all linear combinations
    $I={\left\{Q_{1}P_{1}+\cdots +Q_{n}P_{n}\mid Q_{i}\in K[X]\right\}}\,.$
This is an ideal of $K[X]$, as can be checked directly. Due to fact, this ideal is a principal ideal, hence,
    $I=(E)\,$
with a certain polynomial $E$. This $E$ is a common divisor of the $P_{i}$. Because of $P_{i}\in I=(E)$, we have
    $P_{i}=H_{i}E\,,$
that is $E$ is a factor of every $P_{i}$. A similar reasoning shows
    $P_{i}\in (G)\,$
for all $i$, and, therefore, also
    $(E)=I\subseteq (G)\,.$
Hence,
    $E=GF\,.$
By the condition, $G$ has the maximal degree among all common divisors. Therefore, $F\neq 0$ is a constant. Thus, we have
    $(G)=(E)=I\,,$
and, in particular, $G\in I$. Therefore, $G$ is a linear combination of the $P_{i}$.
# Polynomial ring/Field/Lemma of Bezout/Coprime/Fact

Let $K$ be a field and let $P_{1},\ldots ,P_{n}$ denote coprime polynomials over $K$.
    $Q_{1}P_{1}+\cdots +Q_{n}P_{n}=1\,$
with
$Q_{1},\ldots ,Q_{n}\in K[X]$
# Polynomial ring/Field/Lemma of Bezout/Coprime/Fact/Proof

This follows directly from fact.
# Polynomial ring/Field/Lemma of Bezout/Determining greatest common divisor/Remark

For given polynomials $P_{1},\ldots ,P_{n}\in K[X]$, we can determine explicitly their greatest common divisor $G$ and a representation
    $G=Q_{1}P_{1}+\cdots +Q_{n}P_{n}\,$
as stated in fact. For this, we restrict ourselves to the case $n=2$. Let the degree of $P_{1}$ be as large as the degree of $P_{2}$. The division with remainder
yields
    $P_{1}=P_{2}H_{2}+R_{2}\,$
with a remaining polynomial, whose degree is smaller than the degree of $P_{2}$, or which is $0$. The main point is that the ideals
    $(P_{1},P_{2})=(P_{2},R_{2})\,$
are identical and, thus, the greatest common divisor of $P_{1}$ and $P_{2}$ and of $P_{2}$ and $R_{2}$ coincide. Now we perform again the division with remainder, dividing $P_{2}$ by $R_{2}$ with remainder $R_{3}$, and again the ideal $(R_{2},R_{3})$ coincides with the starting ideal. In this way, we obtain a sequence of remaining polynomials
    $R_{0}=P_{1},R_{1}=P_{2},R_{2},\ldots ,R_{k}\neq 0,0,$
with the property that two adjacent polynomials generate the same ideal. Hence, $R_{k}$ (the last remaining polynomial different from $0$) is the greatest common divisor of $R_{0}$ and $R_{1}$. We can find a representation of $R_{k}$ as a linear combination of the $R_{0},R_{1}$, by working back this algorithm using the equations which describe the divisions with remainder.
# Divisibility theory (Z)/Lemma of Bezout/Fact

Every set of integers $a_{1},\ldots ,a_{n}$
$d$
$d$
$a_{1},\ldots ,a_{n}$
$r_{1},\ldots ,r_{n}$
    $r_{1}a_{1}+r_{2}a_{2}+\cdots +r_{n}a_{n}=d\,.$
In particular, for coprime integers $a_{1},\ldots ,a_{n}$, there exists a representation of $1$.
# Vector space/Linear mapping/Generalized eigenspace/Definition

For a linear mapping $\varphi$ on a $K$-vector space $V$ and an eigenvalue $\lambda \in K$,
    $\operatorname {GeEig} _{\lambda }(\varphi )=\bigcup _{n\in \mathbb {N} }\operatorname {kern} {\left(\varphi -\lambda \operatorname {Id} \right)}^{n}\,$
is called generalized eigenspace of $\varphi$ for this eigenvalue.
# Characteristic polynomial/Coprime factorization/Direct sum/Fact/Proof

Due to the Lemma of Bezout, there exist polynomials $S,T\in K[T]$ such that
    $SP+TQ=1\,.$
Set $U=\operatorname {kern} P(\varphi )$ and $W=\operatorname {kern} Q(\varphi )$. Let $v\in V$. Due to the Theorem of Cayley-Hamilton , we have
    $0=\chi _{\varphi }(\varphi )=(P(\varphi )\circ Q(\varphi ))(v)=P(\varphi )(Q(\varphi )(v))\,.$
Therefore, the image of $Q(\varphi )$ belongs to the kernel of $P(\varphi )$ and vice versa. From
    ${\begin{aligned}v&=\operatorname {Id} _{V}(v)\\&=(SP+TQ)(\varphi )(v)\\&=S(\varphi )(P(\varphi )(v))+T(\varphi )(Q(\varphi )(v))\\&=P(\varphi )(S(\varphi )(v))+Q(\varphi )(T(\varphi )(v))\end{aligned}}$
we can read off that the left-hand summand belongs to $\operatorname {Im} P(\varphi )\subseteq \operatorname {kern} Q(\varphi )$ and the right-hand summand belongs to $\operatorname {Im} Q(\varphi )\subseteq \operatorname {kern} P(\varphi )$. Therefore, we have a sum decomposition, which is direct, since $P(\varphi )(v)=Q(\varphi )(v)=0$ implies $v=0$. For the $\varphi$-invariance of these spaces, see exercise. For $v\in \operatorname {kern} Q(\varphi )$, we have
    $v=S(\varphi )(P(\varphi )(v))+T(\varphi )(Q(\varphi )(v))=S(\varphi )(P(\varphi )(v))=P(\varphi )(S(\varphi )(v))\,,$
that is, we have $\operatorname {Im} P(\varphi )=\operatorname {kern} Q(\varphi )$. Therefore, the restriction of $P(\varphi )$ to the kernel of $Q(\varphi )$ is surjective, thus bijective.
# ACR/Life before Life

Life before Life When somebody scientifically talks about life than he usually refers to life on earth. To recreate what has been before life on earth existed another approach needs to be taken. Here the approach is to assume a universe filled with single matter and build up from this stage to the very complicated stage of life today. You are invited to create your own version of evolution. How to do it Use the pointers below to start. Use your common knowledge, your observation of the environment and its happenings and connect them together to a logical world which can actually exist. Do not try to find scientific references, which follow a different path and are usually open ended.
Do not introduce mathematics here. Everything, what happens in life, could be explained through mathematics but cannot encompass all possibilities which happens in real life and is therefore only of specific use until life has been explained first. Feel free to use known scientific terms for your equivalent meanings to provide some references for a better understanding. But rather give it another name if your meaning diverse too much (proves to be confusing) from the original. The other articles of ACR have done just this and can be a comparison on what you could discover.
Starting points: Movement is life Matter provides the movement Passed on movement is like passing on a meaning - communication Matter provides the environment for other matter The environment restricts the movement of matter it surrounds - applies pressure Restricted moving matter shares its movement with other restricted matter The combining of movements creates other matter forms - matter is growing Grown matter moves in different forms Different movements, passed on, communicate different meanings The formation of different matter-forms is the reaction to the circumstances which is like learning Learning is the fundament of intelligence With the growing of matter the environment changes As matter reacts to its changed environment it grows (adapts) in many forms and the intelligence grows with the matter.
# 2021 annual meeting: New Orleans, LA
## Business at the SIG Meeting
### 2. Dues

Dues are $20/year for faculty and students are requested to contribute what they can. Submit payment online via PayPal, to Lauren's GMail account (see email).

### 3. Follow-up from previous suggestions for improving listserv

* Create a list: Name, email, current projects
* When preparing talks, compile symposiums. SIG members could submit talks, and the SIG can compile symposiums and submit.
* Sending around information, job offers, etc
* Organizing ABCT bipolar SIG at ISBD
Next meeting is in Chicago in June; poster submissions due in January
* Build BD assessment battery matrix
Need a "water carrier" for this -- have multiple meta-analyses that would inform decisions.
* Recommendations for core measures for a standard, including neurocognition

### 4. Symposium submissions

* Symposium submissions
# ACR/ACR&Brain
## The functions of the brain

* Interface between body and environment
* Store
* Recall
* Compare

## Interface between body and environment

The occurrence of the brain in some living species and not in other ones lead to the conclusion that it is not a necessity for the body to function properly as an entity. Although some of the functions which a brain provides might be necessary to enable a living creature to survive, if they are just simple mechanical, repeatable functions of a body part then they might be served of just a provision which stores exactly this functionality. But does not necessary need a brain with all the other functionalities. Only when this function need to be different when the circumstances are different and need to be adapted to the circumstances then a brain might be necessary. Depending on the complexity, size and amount of this functionalities the brain needs to be flexible too in its size.

## Store

In order to provide all the functionality which are necessary to adapt the body to its environment the brain must to be able to store all the information which it gets from the body and from the environment. Since this storage is not controlled by any other part of the body, or of just a part of the brain, it needs to be controlled by the way the brain is built.
There are two main features which indicates how the brain could work. One is that there is an existence of complementary brain parts and the other is the vast amount of neurons connected with even a greater amount of axons (connections between the neurons).
To keep track of an information stored in many neurons, which are connected with many other neurons which have nothing to do with the information, seem only possible if done sequentially. In a way which is known in computer programming as 'linked list'. Which means that every part of the information, stored in one neuron, has also an information on where to find the next part of the information. And when all the information is collected (action+circumstances) then the last neuron has the information where to find the reaction. Which is also stored as a linked list. This additional information is provided when the information is stored the first time and cannot be changed as long as the brain exists. Which would account for the amount needed of neurons and axions.

## Recall

The process of recalling is necessary for many different reasons. The data can be recalled on its own or to manipulate (add, subtract, compare) another data already recalled. If it is recalled for manipulation then it, together with the other recalled data, will provide a new sequence of information which will lead to a different end-neuron which will provide the 'address' of the specific reaction to follow.
To recall information it is necessary that it is precicely known what is being looked for. In this way it can be checked that the right axions are being followed leading to the right neurons and consequently to the right information (address) stored in the last neuron. If this information is not thought after then it might be recalled to provide it for comparison.
# Algebra 1/Unit 3: Linear and Literal Equations, and how to solve them

Here, we will discuss Linear and Literal equations and how to solve them. This lesson might be a bit tricky, but once you master the lesson it will get way more manageable. Let's head onto the lesson.

## Literal Equations

Let's start with the easier one, literal equations. Literal equations typically have a hefty amount of variables. Many of the literal equations you have worked with have been formulas. Although these equations will look different than our normal equations, they still follow the normal rules of solving.

### Examples for "solving" Literal Equations

An example of a literal equation is ${\text{A = b · h}}$, this is the formula for finding the area of a rectangle. We are going to simply "solve" for the variable ${\text{h}}$ from the equation, we solve this by using the order of operations in reverse and adding, subtracting, multiplying, or diving values to both sides of the equation, to make effectively nothing different.
${\text{A = b · h}}$
* When “solving” Literal Equations, we follow the same rules as simple equations. Therefore, in order to solve for ${\text{h}}$ in this equation, we need to isolate it by itself. Therefore, we will divide both sides by ${\text{b}}$
${\frac {A}{b}}={\frac {b\cdot h}{b}}$
* Doing so, the process will isolate ${\text{h}}$, giving us the answer:
${\text{h = }}{\frac {A}{b}}$
Another example of a literal equation is ${\text{x = m + n}}$. We will simply do the same in the last example, isolating ${\text{m}}$.
${\text{x = m + n}}$
* Using the last example as a reference, in order to solve for and or isolate ${\text{m}}$, we will subtract both sides by ${\text{n}}$.
${\text{x}}{\mathit {-n}}{\text{ = m + n}}{\mathit {-n}}$
* ${\text{m}}$ is now isolated.
${\text{x − n = m}}$
${\text{m = x − n}}$
* Even if there were no numbers, we have "solved" the literal equation for ${\text{m}}$
# Algebra 1/Unit 1: Introduction To Algebra/Fractions Quiz

This quiz is meant to advance your fractions skill/review your skills on fractions. If you decide to cheat, it's your own loss, and not ours. Please do the quiz first, then check your answers. Again, cheating is your own loss.
# Benefit corporations

Benefit corporations are a corporate structure that blends for-profit and not-for-profit elements. This is a lesson about benefit corporations.

## Discussion questions and essay ideas

Read the suggested readings below and then find someone to discuss the following questions with.
* Should all businesses be benefit corporations?
* When is it desirable to form a benefit corporation?
* Can benefit corporations be publicly held?

## Readings
### Wikipedia

* Benefit corporation
* B Corporation (certification)
* B Lab
* Workplace spirituality
* Charitable for-profit entity
* Social purpose corporation
* Shareholder value
* Common good
* Public-benefit corporation
* New York state public-benefit corporations
* Socially responsible investing
* Social finance
* Community interest company
* Consumers' co-operative
# Bengali Language/Characteristics of Objects
## Colors

| Color name in English | Color name in Bengali | Transliteration |
| White | সাদা | shaa-daa |
| Black | কালো | kaa-lo |
| Gray | ধূসর | dhu-shawr |
| Violet | বেগুনী | be-gu-ni |
| Blue | নীল | nil |
| Yellow | হলুদ | ho-lud |
| Green | সবুজ | sho-buj |
| Red | লাল | laal |
| Orange | কমলা | kaw-mo-laa |
| Pink | গোলাপী | go-laa-pi |
| Brown | বাদামী / খয়েরী | baa-daa-mi / khaw-ye-ri |
| Golden | সোনালী | sho-naa-li |
| Silver | রূপালী | ru-paa-li |
| Dark | গাঢ় | gaa-rho |
| Light | হালকা | haal-kaa |
| Bright | উজ্জ্বল | uj-jawl |
| Dim | অনুজ্জ্বল | aw-nuj-jawl |
# Benchmarking tools

Benchmarking allows us to measure and comparing different performance metrics from our IT platform. Several tools can be used depending on what part of our infrastructure we want to benchmark.
You can try any of the following tools depending of what part of your infrastructure you want to evaluate:
IO (disks) performance tools:
* w:IOzone
* iometer
* fio, io tester
* dd
See also: RAID
SQL benchmarking tools
* pgbench
* DBench
For generating load on your machine you can user stress --cpu 48 --timeout 60, where cpu is the number of process to spawn depending of the number of your CPU/Cores.
# Bengali Language/Adjectives

Adjectives in Bengali, similar to their English counterparts, do not inflect for gender or case. Additionally, they do not inflect for number either! This means that once you know an adjective, you can apply it to any noun(s) without any consideration.
To take an example, consider the adjective 'tall'; the Bengali word for it is লম্বা ("lambaa"). Observe how the adjective (in bold letters) remains the same in the example below:
| English | Bengali |
| the tall boy | লম্বা ছেলেটা |
| the tall girl | লম্বা মেয়েটা |
| the tall boys | লম্বা ছেলেরা |
| the tall girls | লম্বা মেয়েরা |
Notice how only the definite markers (indicating singular/plural noun) change in the example above. Keep in mind, however, that since the definite markers can be omitted, লম্বা ছেলে can mean "tall boy" or "tall boys"; you will have to use the context to determine which one makes sense.

## Demonstrative Adjectives

We have already seen how demonstrative pronouns (see chapter on pronouns for details) function in Bengali. Demonstrative adjectives follow exactly the same pattern with only one difference: the definite article is attached to the noun instead of the adjective. Let's look at some examples:
| English | Bengali |
| This is mine | এটা আমার |
| This book is mine | এই বইটা আমার |
| That is mine | ওটা আমার |
| That book is mine. | ওই বইটা আমার |
So while the pronouns 'this' and 'that' translated to এটা and ওটা, the demonstrative adjectives translate to এই and ওই, with the definite singular/plural markers attached to the noun following these adjectives. So "this book" is এই বইটা, "these books" is এই বইগুলো; "this boy" is এই ছেলে, and "these boys" is এই ছেলেরা.
# Bengali Language/Belief and religion

| English | Bengali | Transliteration |
| Religion | ধর্ম | dhormo |
| Islam | ইসলাম | islam |
| Islamic | ইসলামী | islami |
| Muslim | মুসলমান | musolman |
| Muslim | মুসলিম | muslim |
| Abrahamic | ইব্রাহিমীয়​ | ibrahimiyo |
| Hinduism | হিন্দুধর্ম/সনাতন ধর্ম | hindudhormo/shonaton dhormo |
| Christianity | খ্রীষ্টধর্ম | khrishtodhormo |
| Christian (person) | খ্রীষ্টান | khrishtan |
| Christian (person) | নাসারা | nasara |
| Christian | খ্রিস্টীয় | khrishtiyo |
| Judaism | ইহুদীধর্ম | ihudidhormo |
| Jewish | ইহুদী | ihudi |
| monotheism | তাওহীদ | taoheed |
| polytheism | শিরিক | shirik |
| atheism | নাস্তিকতা | nastikota |
| atheist | নাস্তিক | nastik |
# BCP/Lobelia cardinalis

Lobelia cardinalis
| Flowers Wikipedia • Commons • Wikibooks (horticulture) • Wikibooks (subject) • Wikispecies • Fruit and seed clock | Profile for Lobelia cardinalis (Cardinal Flower) Identifying Characteristics Recent Logs SBJ 17:20, 27 July 2007 (UTC) SBJ 13:51, 11 August 2007 (UTC) --Jomegat 00:39, 13 August 2007 (UTC) SBJ 10:58, 15 August 2007 (UTC) SBJ 08:31, 25 August 2007 (UTC) SBJ 18:24, 4 September 2007 (UTC) (view all logs) |
Global data:
Regional data: Southeastern Pennsylvania: (cultivated) July, August, September New Hampshire: August
Additional images:
# BCP/Lobelia dortmanna

Lobelia dortmanna
| Wikipedia • Commons • Wikibooks (horticulture) • Wikibooks (subject) • Wikispecies • Fruit and seed clock | Profile for Lobelia dortmanna (Water Lobelia) Identifying Characteristics Habit:Herbaceous ForbFlowers:The flowers are 1–2 cm long, with a five-lobed white to pale pink or pale blue corolla, produced one to ten on an erect raceme held above the water surface.Foliage:The leaves are linear to oblong, 2.5–7.5 cm long, produced in a basal rosette underwater.Stem:70–200 cm tallGrowing Conditions:Freshwater, acidic poolsFruit:The fruit is a capsule 5-10 mm long and 3-5 mm wide, containing numerous small seeds.Life Cycle: Perennial Recent Logs Jomegat 20:35, 10 July 2010 (UTC) (view all logs) |
Global data: Temperate zone season(s): Mid Summer, Late Summer
Regional data: New Hampshire: (native) July, August
Additional images:
* Lobelia dortmanna on the right