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Orthogonal Basis for Range Space of a Matrix
Syntax y = orth(x)
See Also null , svd

Computes an orthogonal basis for the range space of the integer, real, double-precision or complex matrix x. Thus if z = x * w for some column vector w, there is a column vector u such that z = y * u.

If x is an integer matrix, y is double-precision. Otherwise y has the same type as x. The number of rows in y is equal to the number of rows in x and the number of columns in y is equal to the dimension of the range space of x. Each of the columns of the matrix y has norm one and the columns are orthogonal; i.e.;
     I = conj(y)' * y
where I is the identity matrix with the same number of columns as y.

If you enter
     x = {1 , 1 , 1}
     y = orth(x)
O-Matrix will reply
Continuing with
     y' * y
results in