$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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Title

If $T:\mathbb{F}^n\to\mathbb{F}^m$ is a linear transformation, then there is a unique matrix $A\in M_{m, n}(\mathbb{F})$ such that $Ax=Tx$ for all $x\in \mathbb{F}$.
The $j$-th column of $A$ is $Te_{j}$, where $\{e_1, \dots, e_n\}$ is the standard basis for $\mathbb{F}^n$

Concepts

Linear transformations from $\mathbb{F}^n\to\mathbb{F}^m$ are given by matrices.

Hypothesis

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Results

Coming soon

Proof

Coming soon

Title

If $T:\mathbb{F}^n\to\mathbb{F}^m$ is a linear transformation, then there is a unique matrix $A\in M_{m, n}(\mathbb{F})$ such that $Ax=Tx$ for all $x\in \mathbb{F}$.
The $j$-th column of $A$ is $Te_{j}$, where $\{e_1, \dots, e_n\}$ is the standard basis for $\mathbb{F}^n$

Concepts

Linear transformations from $\mathbb{F}^n\to\mathbb{F}^m$ are given by matrices.

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon
FullPage
result
concepts
hypothesis
implications
proof
FullPage
result
concepts
hypothesis
implications
proof

Title

If $T:\mathbb{F}^n\to\mathbb{F}^m$ is a linear transformation, then there is a unique matrix $A\in M_{m, n}(\mathbb{F})$ such that $Ax=Tx$ for all $x\in \mathbb{F}$.
The $j$-th column of $A$ is $Te_{j}$, where $\{e_1, \dots, e_n\}$ is the standard basis for $\mathbb{F}^n$

Concepts

Linear transformations from $\mathbb{F}^n\to\mathbb{F}^m$ are given by matrices.

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon

Title

If $T:\mathbb{F}^n\to\mathbb{F}^m$ is a linear transformation, then there is a unique matrix $A\in M_{m, n}(\mathbb{F})$ such that $Ax=Tx$ for all $x\in \mathbb{F}$.
The $j$-th column of $A$ is $Te_{j}$, where $\{e_1, \dots, e_n\}$ is the standard basis for $\mathbb{F}^n$

Concepts

Linear transformations from $\mathbb{F}^n\to\mathbb{F}^m$ are given by matrices.

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon
FullPage
result
concepts
hypothesis
implications
proof