I have a linear transformation T:R^n->R^n and some basis B for R^n ,and i know the representation matrix of T relative to basis B ,[T]_B.
if i want to find out the representation matrix for T with respect to the standard basis E={e_1,..,e_n} .So i'll just create the matrix
([T]_B*[e_1]_B ,...,[T]_B*[e_n]_B) and that will be the representation matrix of T relative to the standard basis am i right?
if not then what hell?
To apply the transform T to a vector written in the standard basis you normally have to do three things:
>Rewrite the vector into base B
>Apply the T to the rewritten vector
>Transform the result back into base E
Those three operations can all be done with one matrix multiplication each so the composition of those three operations is just applying the product of those matrices.
>>8885712
Yes that's what i meant by [T]_B*[e_i]_B ,i will convert e_i to the coordinates in base B then multiply it with the matrix [T]_B and ill have the i'th vector of the representation matrix of T with relative to base E.
is this what you also meant?
>>8885699
Use LaTeX you dumbfuck.
>>8885719
My baboon mind cant comprehend how LaTeX works
>>8885721
>comes for help
>refuses to make his post readable
>blames it on being stupid
found the retard.
0/10
no latex
i'm given [math][T]_B[/math] and need to find [math][T]_E[/math] ,so [math][T]_E=([T]_B[e_1]_B,...,[T]_B[e_n]_B)[/math] ,where for each [math][T]_B[e_i]_B [/math] is a column vector.