Since GramSchmidt does not take Matrix as an input (I wish it did), I would like to know how to normalize a matrix rows. For example if input matrix is:

M = [  1    2]
       [  3    4]

How do I convert it into

Mn = [ 1/sqrt(5)    2/sqrt(5) ]
         [ 3/5            4/5          ]

Each row of matrix Mn has length of 1.

Thank you.

How do I make "simplify" function to recognize complex exponentials. Maple created some exponentiol functions with a square root of negative expression in the denominator of the exponent. It refuses to simplify it. If I manually edit it, by taking negative sign under the root and adding immaginary number, the simplification works. How do I simplify it without manual edit?

The Eq 33 is manually edited line. Simplify function correctly uses cos function.

The Eq 34 is original expression. I tried to tell maple to assume real numbers hoping that it will wotk, but it did not.