- Thread starter akleron
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You must tell us what the notation \(\displaystyle \large\left[T\right]_C^B\) means. It is not a standard far as I know.I need to show to following two statements:

Tbh, I've got no idea how to start.

Would love some help..

Thanks !!

View attachment 16076

It means apply the function T on v (when v belongs to the span of base B) and than write the coordinate vector of the result over base CYou must tell us what the notation \(\displaystyle \large\left[T\right]_C^B\) means. It is not a standard far as I know.

does it make sense ?

\(\displaystyle \text{Let $T$ be the matrix $T$ expressed in the identity matrix basis.}\\

\text{Then for some matrix $B,~[T]^B = BT$ and likewise $[T]^B_C = CBT$}

\\

\text{so $[T+S]^B_C = CB(T+S) = CBT +CBS = [T]^B_C + [ S]^B_C $ }\)

you can do (ii)