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- Semi-orthogonal_matrix abstract "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 eitherIn the following, consider the case where A is an m × n matrix for m > n.Thenwhich implies the isometry propertyfor all x in Rn.For example,is a semi-orthogonal matrix.A semi-orthogonal matrix A is semi-unitary (either A†A = I or AA† = I) and either left-invertible or right-invertible (left-invertible if it has more rows than columns, otherwise right invertible). As a linear transformation applied from the left, a semi-orthogonal matrix with more rows than columns preserves the dot product of vectors, and therefore acts as an isometry of Euclidean space, such as a rotation or reflection.".
- Semi-orthogonal_matrix wikiPageID "34417095".
- Semi-orthogonal_matrix wikiPageRevisionID "593528283".
- Semi-orthogonal_matrix hasPhotoCollection Semi-orthogonal_matrix.
- Semi-orthogonal_matrix subject Category:Geometric_algebra.
- Semi-orthogonal_matrix subject Category:Matrices.
- Semi-orthogonal_matrix type Abstraction100002137.
- Semi-orthogonal_matrix type Arrangement107938773.
- Semi-orthogonal_matrix type Array107939382.
- Semi-orthogonal_matrix type Group100031264.
- Semi-orthogonal_matrix type Matrices.
- Semi-orthogonal_matrix type Matrix108267640.
- Semi-orthogonal_matrix comment "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 eitherIn the following, consider the case where A is an m × n matrix for m > n.Thenwhich implies the isometry propertyfor all x in Rn.For example,is a semi-orthogonal matrix.A semi-orthogonal matrix A is semi-unitary (either A†A = I or AA† = I) and either left-invertible or right-invertible (left-invertible if it has more rows than columns, otherwise right invertible). ".
- Semi-orthogonal_matrix label "Semi-orthogonal matrix".
- Semi-orthogonal_matrix sameAs m.0h_97b6.
- Semi-orthogonal_matrix sameAs Q7449314.
- Semi-orthogonal_matrix sameAs Q7449314.
- Semi-orthogonal_matrix sameAs Semi-orthogonal_matrix.
- Semi-orthogonal_matrix wasDerivedFrom Semi-orthogonal_matrix?oldid=593528283.
- Semi-orthogonal_matrix isPrimaryTopicOf Semi-orthogonal_matrix.