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m →Uniqueness up to unitary transformations: formula was missing a symbol to be correct |
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The decomposition is not unique:
if <math>\ M = B^* B\ </math> for some <math>\ k \times n\ </math> matrix <math>\ B\ </math> and if <math>\ Q\ </math> is any [[unitary matrix|unitary]] <math>k \times k</math> matrix (meaning <math>\ Q^* Q = Q Q^* = I\ </math>),
then <math>\ M = B^* B = B^* Q^* Q B = A^* A\ </math> for <math>\ A = Q B ~.</math>
However, this is the only way in which two decompositions can differ: The decomposition is unique up to [[unitary transformation]]s.
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