A volume associated with \(m{\times}n\) matrices

DOI10.1016/0024-3795(92)90340-GzbMath0762.15003MaRDI QIDQ1187510

Adi Ben-Israel

Publication date: 22 July 1992

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

compound matricesdeterminantsingular valuesinteger solutionsMoore-Penrose inverseorthogonal projectionsHadamard inequalityexterior productsconvex decompositionsresidue arithmeticborderingfull-rank factorizationabsolute value of the determinantcomplementingcounting spanning of trees in a digraphprincipal angles between subspaces

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items

The Moore idempotents of a matrix ⋮ Generalized inverses with proportional minors ⋮ Reflexive generalized inverses and their minors^* ⋮ Dimensionality reduction and volume minimization -- generalization of the determinant minimization criterion for reduced rank regression problems ⋮ Two consequences of Minkowski's \(2^ n\) theorem ⋮ A geometrical interpretation of the inverse matrix ⋮ Product cosines of angles between subspaces ⋮ The determinal rank idempotents of a matrix ⋮ On the convergence of power scaled Cesàro sums ⋮ Properties of the multidimensional finite elements ⋮ Subspaces, angles and pairs of orthogonal projections ⋮ Integral representations for the class of generalized metaplectic operators ⋮ New proofs of two representations and minor of generalized inverse \(A_{T,S}^{(2)}\) ⋮ Adjoints of a matrix ⋮ Singular values and maximum rank minors of generalized inverses ⋮ Moore-penrose inverse of the incidence matrix of a tree ⋮ Unnamed Item ⋮ A practical approach to the secure computation of the Moore-Penrose pseudoinverse over the rationals ⋮ Rank revealing Gaussian elimination by the maximum volume concept ⋮ The geometry of the set of scaled projections ⋮ Full-rank representation of generalized inverse \(A_{T,S}^{(2)}\) and its application ⋮ Unnamed Item ⋮ Determinantal representation of weighted generalized inverses ⋮ The geometry of basic, approximate, and minimum-norm solutions of linear equations ⋮ Determinantal representation of the generalized inverse\bi A_{T,S}^{(2)}over integral domains and its applications ⋮ Refinements of the Hadamard and Cauchy-Schwarz inequalities with two inequalities of the principal angles ⋮ On the existence and computation of rank-revealing LU factorizations ⋮ The classical adjoint ⋮ An application of the matrix volume in probability ⋮ Volume and variance in the linear statistical model ⋮ Matrix Perturbation and Optimal Partition Invariancy in Linear Optimization ⋮ Minors of the Moore-Penrose inverse ⋮ Outer inverses: Jacobi type identities and nullities of submatrices ⋮ On \(l_ p\)-approximate solutions of linear equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A geometric property of the least squares solution of linear equations
• On principal angles between subspaces in \(\mathbb{R}^n\)
• Minors of the Moore-Penrose inverse
• Three results in connection with inverse matrices
• Die exakte Berechnung der Moore-Penrose-Inversen einer Matrix durch Residuenarithmetik
• On extensions of Cramer's rule for solutions of restricted linear systems¹
• Then-dimensional pythagorean theorem
• A unified exposition of some classical matrix theorems
• Bordered Matrices