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

Description
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.

Example
If you enter ```      x = {1 , 1 , 1}      y = orth(x)      y ``` O-Matrix will reply ```      {      -0.57735      -0.57735      -0.57735      } ``` Continuing with ```      y' * y ``` results in ```      1 ```