Razlika između inačica stranice »Inverzna matrica«
| (Nije prikazano 7 međuinačica istog suradnika) | |||
| Redak 34: | Redak 34: | ||
|definicija= The inverse of a square matrix <math>A</math> is a matrix <math>A^{-1}</math> such that <math>AA^{-1}=A^{-1}A=I</math>, where <math>I</math> is the identity matrix. | |definicija= The inverse of a square matrix <math>A</math> is a matrix <math>A^{-1}</math> such that <math>AA^{-1}=A^{-1}A=I</math>, where <math>I</math> is the identity matrix. | ||
|cite= Stover, Christopher and Weisstein, Eric W. "Matrix Inverse." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/MatrixInverse.html | |cite= Stover, Christopher and Weisstein, Eric W. "Matrix Inverse." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/MatrixInverse.html | ||
| − | |napomena=A square matrix <math>A</math> has an inverse iff the determinant <math>\left | + | |napomena=A square matrix <math>A</math> has an inverse iff the determinant <math> det\left ( A \right )\neq 0</math> |
|see_also=Gauss-Jordan Elimination, Gaussian Elimination, LU Decomposition, Matrix, Matrix 1-Inverse, Matrix Addition, Matrix Multiplication, Moore-Penrose Matrix Inverse, Nonsingular Matrix, Pseudoinverse, Singular Matrix, Strassen Formulas | |see_also=Gauss-Jordan Elimination, Gaussian Elimination, LU Decomposition, Matrix, Matrix 1-Inverse, Matrix Addition, Matrix Multiplication, Moore-Penrose Matrix Inverse, Nonsingular Matrix, Pseudoinverse, Singular Matrix, Strassen Formulas | ||
|primjeri= | |primjeri= | ||
}} | }} | ||
Trenutačna izmjena od 18:50, 1. listopada 2016.
Definicija: matrica čija su oba umnoška nje i zadane matrice jednaka jediničnoj matrici
Napomena: Neka je \(A\) kvadratna matrica. Kažemo da je matrica \(B\) inverzna matrica matrice \(A\) ako je \(AB=BA=I\), pri čemu je \(I\) jedinična matrica. Matricu B označujemo kao \(A^{-1}\). Dakle, vrijedi \(AA^{-1}=A^{-1}A=I\)
Povezani pojmovi: matrica, adjungirana matrica, transponirana matrica, Jordanova matrica, kvadratna matrica, matrica prijelaza, matrica susjedstva
Simbol: \(A^{-1}\)
Engleske istovrijednice: reciprocal matrix, matrix inverse
Struna ID: 32321
Obrađivač: Magdalena Igaly
Faza obrade: zaključaj naziv
Vrsta riječi: imenica Rod: ženski Broj: jednina
Cilj projekta "Hrvatsko nazivlje u matematici" je na jednom mjestu prikupiti i obraditi sve hrvatske nazive koji na izravan ili neizravan način imaju veze s matematikom. Ako želite na bilo koji način doprinijeti ostvarenju ciljeva ovog projekta, molim javite se voditelju projekta na adresu goran.igaly@math.hr
WMW naziv: matrix inverse
WMW klasifikacija: Algebra > Linear Algebra > Matrices > Matrix Operations >
WMW definicija: The inverse of a square matrix \(A\) is a matrix \(A^{-1}\) such that \(AA^{-1}=A^{-1}A=I\), where \(I\) is the identity matrix.
WMW napomena: A square matrix \(A\) has an inverse iff the determinant \( det\left ( A \right )\neq 0\)
WMW See also: Gauss-Jordan Elimination, Gaussian Elimination, LU Decomposition, Matrix, Matrix 1-Inverse, Matrix Addition, Matrix Multiplication, Moore-Penrose Matrix Inverse, Nonsingular Matrix, Pseudoinverse, Singular Matrix, Strassen Formulas
Izvor: Stover, Christopher and Weisstein, Eric W. "Matrix Inverse." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/MatrixInverse.html
Struna ID: 32321