$ \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}} $
FullPage
definition
concepts
used in
hypothesis
results
Let $V$ and $W$ be finite dimensional vector spaces over $\mathbb{F}$ and let $T:V\to W$ be a linear transformation. Let $B=\{v_1, \dots, v_n\}$ and $C=\{w_1, \dots, w_m\}$ be basis for $V$ and $W$, respectively. For each $j$, we write $Tv_i=\sum_{i=1}^m a_{ij}w_j$. Then the matrix $A=[a_{ij}]$ is the matrix representation of $T$ from $B$ to $C$, and completely encodes $T$. It is denoted $$\begin{align*} A=[T]_{C\leftarrow B} \end{align*}$$

Concepts

The letter in the brakets denotes the transformation, as usual. The subscript tells you that 'this transformation is more specifically specifically a transformation that will change a vector from the $B$ basis to the $C$ basis'

Used In

Coming soon

Hypothesis

Coming soon

Results

Coming soon
Let $V$ and $W$ be finite dimensional vector spaces over $\mathbb{F}$ and let $T:V\to W$ be a linear transformation. Let $B=\{v_1, \dots, v_n\}$ and $C=\{w_1, \dots, w_m\}$ be basis for $V$ and $W$, respectively. For each $j$, we write $Tv_i=\sum_{i=1}^m a_{ij}w_j$. Then the matrix $A=[a_{ij}]$ is the matrix representation of $T$ from $B$ to $C$, and completely encodes $T$. It is denoted $$\begin{align*} A=[T]_{C\leftarrow B} \end{align*}$$

Concepts

The letter in the brakets denotes the transformation, as usual. The subscript tells you that 'this transformation is more specifically specifically a transformation that will change a vector from the $B$ basis to the $C$ basis'

Used In

Coming soon

Hypothesis

Coming soon

Results

Coming soon
FullPage
definition
concepts
used in
hypothesis
results
FullPage
definition
concepts
used in
hypothesis
results
Let $V$ and $W$ be finite dimensional vector spaces over $\mathbb{F}$ and let $T:V\to W$ be a linear transformation. Let $B=\{v_1, \dots, v_n\}$ and $C=\{w_1, \dots, w_m\}$ be basis for $V$ and $W$, respectively. For each $j$, we write $Tv_i=\sum_{i=1}^m a_{ij}w_j$. Then the matrix $A=[a_{ij}]$ is the matrix representation of $T$ from $B$ to $C$, and completely encodes $T$. It is denoted $$\begin{align*} A=[T]_{C\leftarrow B} \end{align*}$$

Concepts

The letter in the brakets denotes the transformation, as usual. The subscript tells you that 'this transformation is more specifically specifically a transformation that will change a vector from the $B$ basis to the $C$ basis'

Used In

Coming soon

Hypothesis

Coming soon

Results

Coming soon
Let $V$ and $W$ be finite dimensional vector spaces over $\mathbb{F}$ and let $T:V\to W$ be a linear transformation. Let $B=\{v_1, \dots, v_n\}$ and $C=\{w_1, \dots, w_m\}$ be basis for $V$ and $W$, respectively. For each $j$, we write $Tv_i=\sum_{i=1}^m a_{ij}w_j$. Then the matrix $A=[a_{ij}]$ is the matrix representation of $T$ from $B$ to $C$, and completely encodes $T$. It is denoted $$\begin{align*} A=[T]_{C\leftarrow B} \end{align*}$$

Concepts

The letter in the brakets denotes the transformation, as usual. The subscript tells you that 'this transformation is more specifically specifically a transformation that will change a vector from the $B$ basis to the $C$ basis'

Used In

Coming soon

Hypothesis

Coming soon

Results

Coming soon
FullPage
definition
concepts
used in
hypothesis
results