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Algèbre linéaire

Équations linéaires, valeurs propres, valeurs singulières, décomposition, opérations matricielles, structure de la matrice

Les fonctions d’algèbre linéaire de MATLAB® permettent d’effectuer rapidement des calculs matriciels d’une grande robustesse numérique. Les fonctionnalités disponibles comprennent, entre autres, diverses factorisations matricielles, la résolution d’équations linéaires et le calcul de valeurs propres ou singulières. Pour une introduction, consultez Matrices dans l’environnement MATLAB.

Fonctions

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mldivideSolve systems of linear equations Ax = B for x
mrdivideSolve systems of linear equations xA = B for x
pagemldividePage-wise left matrix divide (depuis R2022a)
pagemrdividePage-wise right matrix divide (depuis R2022a)
decompositionMatrix decomposition for solving linear systems
lsqminnormMinimum norm least-squares solution to linear equation
linsolveSolve linear system of equations
invInverse de matrice
pageinvPage-wise matrix inverse (depuis R2022a)
pinvMoore-Penrose pseudoinverse
lscovLeast-squares solution in presence of known covariance
lsqnonnegSolve nonnegative linear least-squares problem
sylvesterSolve Sylvester equation AX + XB = C for X
eigEigenvalues and eigenvectors
pageeigPage-wise eigenvalues and eigenvectors (depuis R2023a)
eigsSubset of eigenvalues and eigenvectors
balanceDiagonal scaling to improve eigenvalue accuracy
svdSingular value decomposition
pagesvdPage-wise singular value decomposition (depuis R2021b)
svdsSubset of singular values and vectors
svdsketchCompute SVD of low-rank matrix sketch (depuis R2020b)
gsvdGeneralized singular value decomposition
ordeigEigenvalues of quasitriangular matrices
ordqzReorder eigenvalues in QZ factorization
ordschurReorder eigenvalues in Schur factorization
polyeigPolynomial eigenvalue problem
qzQZ factorization for generalized eigenvalues
hessHessenberg form of matrix
schurSchur decomposition
rsf2csfConvert real Schur form to complex Schur form
cdf2rdfConvert complex diagonal form to real block diagonal form
luLU matrix factorization
ldlBlock LDL' factorization for Hermitian indefinite matrices
cholCholesky factorization
cholupdateRank 1 update to Cholesky factorization
qrQR decomposition
qrdeleteRemove column or row from QR factorization
qrinsertInsert column or row into QR factorization
qrupdateRank 1 update to QR factorization
planerotGivens plane rotation
transposeTransposer un vecteur ou une matrice
ctransposeComplex conjugate transpose
pagetransposePage-wise transpose (depuis R2020b)
pagectransposePage-wise complex conjugate transpose (depuis R2020b)
mtimesMatrix multiplication
pagemtimesPage-wise matrix multiplication (depuis R2020b)
mpowerMatrix power
sqrtmMatrix square root
expmMatrix exponential
logmMatrix logarithm
funmEvaluate general matrix function
kronKronecker tensor product
crossCross product
dotDot product
bandwidthLower and upper matrix bandwidth
trilLower triangular part of matrix
triuUpper triangular part of matrix
isbandedDetermine if matrix is within specified bandwidth
isdiagDetermine if matrix is diagonal
ishermitianDetermine if matrix is Hermitian or skew-Hermitian
issymmetricDetermine if matrix is symmetric or skew-symmetric
istrilDetermine if matrix is lower triangular
istriuDetermine if matrix is upper triangular
normNormes de vecteurs et de matrices
pagenormPage-wise matrix or vector norm (depuis R2022b)
normest2-norm estimate
vecnormVector-wise norm
condCondition number for inversion
condest1-norm condition number estimate
rcondReciprocal condition number
condeigCondition number with respect to eigenvalues
detMatrix determinant
nullNull space of matrix
orthOrthonormal basis for range of matrix
rankRank of matrix
rrefReduced row echelon form (Gauss-Jordan elimination)
traceSum of diagonal elements
subspaceAngle between two subspaces

Rubriques