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- Invertible_matrix abstract "In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such thatwhere In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A and is called the inverse of A, denoted by A−1. A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is 0. Singular matrices are rare in the sense that a square matrix randomly selected from a continuous uniform distribution on its entries will almost never be singular.Non-square matrices (m-by-n matrices for which m ≠ n) do not have an inverse. However, in some cases such a matrix may have a left inverse or right inverse. If A is m-by-n and the rank of A is equal to n, then A has a left inverse: an n-by-m matrix B such that BA = I. If A has rank m, then it has a right inverse: an n-by-m matrix B such that AB = I.Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.While the most common case is that of matrices over the real or complex numbers, all these definitions can be given for matrices over any commutative ring. However, in this case the condition for a square matrix to be invertible is that its determinant is invertible in the ring, which in general is a much stricter requirement than being nonzero. The conditions for existence of left-inverse resp. right-inverse are more complicated since a notion of rank does not exist over rings.".
- Invertible_matrix wikiPageExternalLink books?id=jgEiuHlTCYcC&printsec=frontcover.
- Invertible_matrix wikiPageExternalLink InverseMatrixMod.html.
- Invertible_matrix wikiPageExternalLink demo.html.
- Invertible_matrix wikiPageExternalLink lapack.
- Invertible_matrix wikiPageExternalLink mws_gen_sle_bck_system.pdf.
- Invertible_matrix wikiPageExternalLink lecture-3-multiplication-and-inverse-matrices.
- Invertible_matrix wikiPageExternalLink eigen.
- Invertible_matrix wikiPageExternalLink inverse-of-matrix-calculator.
- Invertible_matrix wikiPageExternalLink matrixinv.php.
- Invertible_matrix wikiPageExternalLink inverse-matrix--part-1?playlist=Linear+Algebra.
- Invertible_matrix wikiPageExternalLink www.solvingequations.net.
- Invertible_matrix wikiPageExternalLink cc_matrix_pseudoinv.html.
- Invertible_matrix wikiPageID "217122".
- Invertible_matrix wikiPageRevisionID "606447752".
- Invertible_matrix hasPhotoCollection Invertible_matrix.
- Invertible_matrix id "6362".
- Invertible_matrix id "p/i052440".
- Invertible_matrix title "Derivative of inverse matrix".
- Invertible_matrix title "Inversion of a matrix".
- Invertible_matrix subject Category:Determinants.
- Invertible_matrix subject Category:Linear_algebra.
- Invertible_matrix subject Category:Matrices.
- Invertible_matrix subject Category:Matrix_theory.
- Invertible_matrix type Abstraction100002137.
- Invertible_matrix type Arrangement107938773.
- Invertible_matrix type Array107939382.
- Invertible_matrix type Cognition100023271.
- Invertible_matrix type CognitiveFactor105686481.
- Invertible_matrix type Determinant105692419.
- Invertible_matrix type Determinants.
- Invertible_matrix type Group100031264.
- Invertible_matrix type Matrices.
- Invertible_matrix type Matrix108267640.
- Invertible_matrix type PsychologicalFeature100023100.
- Invertible_matrix comment "In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such thatwhere In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A and is called the inverse of A, denoted by A−1. A square matrix that is not invertible is called singular or degenerate.".
- Invertible_matrix label "Inverse matrix".
- Invertible_matrix label "Invertible matrix".
- Invertible_matrix label "Macierz odwrotna".
- Invertible_matrix label "Matrice inversible".
- Invertible_matrix label "Matrice invertibile".
- Invertible_matrix label "Matriz inversa".
- Invertible_matrix label "Matriz invertible".
- Invertible_matrix label "Reguläre Matrix".
- Invertible_matrix label "Обратная матрица".
- Invertible_matrix label "معكوس مصفوفة".
- Invertible_matrix label "正則行列".
- Invertible_matrix label "逆矩阵".
- Invertible_matrix sameAs Regulární_matice.
- Invertible_matrix sameAs Reguläre_Matrix.
- Invertible_matrix sameAs Matriz_invertible.
- Invertible_matrix sameAs Matrice_inversible.
- Invertible_matrix sameAs Matrice_invertibile.
- Invertible_matrix sameAs 正則行列.
- Invertible_matrix sameAs 가역행렬.
- Invertible_matrix sameAs Inverse_matrix.
- Invertible_matrix sameAs Macierz_odwrotna.
- Invertible_matrix sameAs Matriz_inversa.
- Invertible_matrix sameAs m.01fsnz.
- Invertible_matrix sameAs Q242188.
- Invertible_matrix sameAs Q242188.
- Invertible_matrix sameAs Invertible_matrix.
- Invertible_matrix wasDerivedFrom Invertible_matrix?oldid=606447752.
- Invertible_matrix isPrimaryTopicOf Invertible_matrix.