is an isometry where U is given, U is known to be a unitary and W is a given. Thus, we are trying to solve the following collection of equations for x.
Now, of course, since is invertible, x = 0. Let us see how NCProcess1 behaves on the equations of (§). NCProcess1 creates the following output which we call a ``spreadsheet''. The appearing in the spreadsheet below may be read as equal sign.
|YOUR SESSION HAS DIGESTED|
|THE FOLLOWING RELATIONS|
U* U 1
W* W 1
|USER CREATIONS APPEAR BELOW|
|SOME RELATIONS WHICH APPEAR BELOW|
|MAY BE UNDIGESTED|
The polynomials listed in the spreadsheet above generated the same ideal as (§). Therefore, any solution to (§) is a solution of the equations in the spreadsheet and vice-versa. Therefore, if U is unitary, then the matrix in (§) is an isometry if and only if x is the zero matrix and W is an isometry.