Quick review

basis transforamtion

Linear Transformation

Transition matrix

\[ B'[I]^{B'}_{B} = B \] \( B \text{ is transition to } B' \)
\([I]^{B'}_{B}\) is a transition matrix.
Quick review Coordinate Vector && Transition Matrix
Something Unsorted

Coordinate Matrix

\[ w=B[w]_{B} \] \( w= \begin{bmatrix} 4 \\ 7 \end{bmatrix} \)
\( B= \begin{bmatrix} 2 & 3 \\ 5 & 7 \end{bmatrix} \)
\( [w]_{B}= \begin{bmatrix} -7 \\ 6 \end{bmatrix} \)

Standard matrix


Coordinate Vector


Matrix representation of T


Standard Matrix


Formula Change


Combination of linear transformation


Inverse function