Thread: inner product spaces

Can you please, help me with this
Suppose V and W are finite dimensional inner product spaces with orthogonal bases B1 and B2, respectively. Let T: V->W is linear, so we know that T*: V->W (linear) exists and is unique. Prove that [T*]_B1,B2 is the conjugate transpose of [T*]_B2,B1.
Thank you!

Originally Posted by bamby

Suppose V and W are finite dimensional inner product spaces with orthogonal bases B1 and B2, respectively. Let T: V->W is linear, so we know that T*: V->W (linear) exists and is unique. Prove that [T]_B1,B2 is the conjugate transpose of [T*]_B2,B1.

Suppose that B_1 consists of vectors , and B_2 consists of vectors . Then . In other words, the (j,i)-element of is the complex conjugate of the (i,j)-element of .