Let F be the linear transformation that switches for and vice versa. Find the transformation matrix A for this linear transformation.
Then find the vectors so that and . Choose this as a basis, and then find F's transformation matrix in this basis.
Let F be the linear transformation that switches for and vice versa. Find the transformation matrix A for this linear transformation.
Then find the vectors so that and . Choose this as a basis, and then find F's transformation matrix in this basis.
so we have and which gives you hence
let we want to have and thus so we may choose
Then find the vectors so that and . Choose this as a basis, and then find F's transformation matrix in this basis.
the matrix of F in this new basis is obviously:
remember: if then would be the j-th column of the matrix of F with respect to the basis