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About: Semi-orthogonal matrix     Goto   Sponge   NotDistinct   Permalink

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In linear algebra, a semi-orthogonal matrix is a non-square matrix with real entries where: if the number of columns exceeds the number of rows, then the rows are orthonormal vectors; but if the number of rows exceeds the number of columns, then the columns are orthonormal vectors. Equivalently, a non-square matrix A is semi-orthogonal if either In the following, consider the case where A is an m × n matrix for m > n.Then The fact that implies the isometry property for all x in Rn. For example, is a semi-orthogonal matrix.