Effect of multiplying a matrix by a diagonal matrix.
Q. What is the effect of pre-multiplying a matrix
by a diagonal matrix
A. The effect is that of multiplying the i-th row of matrix A by the factor
i.e. the successive
rows of the original matrix are simply multiplied by successive diagonal elements of the diagonal
matrix. Explicitly:
Q. What is the effect of post-multiplying a matrix
by a diagonal matrix
A. The effect is that of multiplying the i-th column of matrix A by the factor
i.e. the
successive columns of the original matrix are simply multiplied by successive diagonal elements
of the diagonal matrix. Explicitly:
