# Finding the matrix with respect to two bases

## Homework Statement

If I am giving a matrix A representing the linear transformation L(x) = Ax, then A is the matrix-representation of L with respect to the basis elements in the vector-space S (standard).

If I am now given another vectorspace V by the matrix V, and I want to find the matrix B representing L with respect to the bases S and V, I use:

B = V^(-1) * S.

## The Attempt at a Solution

Is what I wrote correct?

Sincerly, Niles.

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## Homework Statement

If I am giving a matrix A representing the linear transformation L(x) = Ax, then A is the matrix-representation of L with respect to the basis elements in the vector-space S (standard).

If I am now given another vectorspace V by the matrix V, and I want to find the matrix B representing L with respect to the bases S and V, I use:

B = V^(-1) * S.

## The Attempt at a Solution

Is what I wrote correct?