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About: EP matrix     Goto   Sponge   NotDistinct   Permalink

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In mathematics, an EP matrix (or range-Hermitian matrix or RPN matrix) is a square matrix A whose range is equal to the range of its conjugate transpose A*. Another equivalent characterization of EP matrices is that the range of A is orthogonal to the nullspace of A. Thus, EP matrices are also known as RPN (Range Perpendicular to Nullspace) matrices. The range of any matrix A is perpendicular to the null-space of A*, but is not necessarily perpendicular to the null-space of A. When A is an EP matrix, the range of A is precisely perpendicular to the null-space of A.