# Algebra lineare

Equazioni lineari, autovalori, valori singolari, decomposizione, operazioni matriciali, struttura delle matrici

Le funzioni di algebra lineare in MATLAB® forniscono calcoli matriciali rapidi e numericamente robusti. Le funzionalità includono una serie di fattorizzazioni matriciali, la risoluzione di equazioni lineari, il calcolo di autovalori o valori singolari e altro ancora. Per un’introduzione, vedere Le matrici nell'ambiente di MATLAB.

## Funzioni

espandi tutto

 `mldivide` Solve systems of linear equations Ax = B for x `mrdivide` Solve systems of linear equations xA = B for x `pagemldivide` Page-wise left matrix divide (Da R2022a) `pagemrdivide` Page-wise right matrix divide (Da R2022a) `decomposition` Matrix decomposition for solving linear systems `lsqminnorm` Minimum norm least-squares solution to linear equation `pagelsqminnorm` Page-wise minimum-norm least-squares solution to linear equation (Da R2024a) `linsolve` Solve linear system of equations `inv` Inverso delle matrici `pageinv` Page-wise matrix inverse (Da R2022a) `pinv` Moore-Penrose pseudoinverse `pagepinv` Page-wise Moore-Penrose pseudoinverse (Da R2024a) `lscov` Least-squares solution in presence of known covariance `lsqnonneg` Solve nonnegative linear least-squares problem `sylvester` Solve Sylvester equation AX + XB = C for X
 `eig` Eigenvalues and eigenvectors `pageeig` Page-wise eigenvalues and eigenvectors (Da R2023a) `eigs` Subset of eigenvalues and eigenvectors `balance` Diagonal scaling to improve eigenvalue accuracy `svd` Singular value decomposition `pagesvd` Page-wise singular value decomposition (Da R2021b) `svds` Subset of singular values and vectors `svdsketch` Compute SVD of low-rank matrix sketch (Da R2020b) `svdappend` Revise SVD after appending data (Da R2023b) `gsvd` Generalized singular value decomposition `ordeig` Eigenvalues of quasitriangular matrices `ordqz` Reorder eigenvalues in QZ factorization `ordschur` Reorder eigenvalues in Schur factorization `polyeig` Polynomial eigenvalue problem `qz` Generalized Schur (QZ) factorization for generalized eigenvalues `hess` Hessenberg form of matrix `schur` Schur decomposition `rsf2csf` Convert real Schur form to complex Schur form `cdf2rdf` Convert complex diagonal form to real block diagonal form
 `lu` LU matrix factorization `ldl` Block LDL' factorization for Hermitian indefinite matrices `chol` Cholesky factorization `cholupdate` Rank 1 update to Cholesky factorization `qr` QR decomposition `qrdelete` Remove column or row from QR factorization `qrinsert` Insert column or row into QR factorization `qrupdate` Rank 1 update to QR factorization `planerot` Givens plane rotation
 `transpose` Trasporre un vettore o una matrice `ctranspose` Complex conjugate transpose `pagetranspose` Page-wise transpose (Da R2020b) `pagectranspose` Page-wise complex conjugate transpose (Da R2020b) `mtimes` Matrix multiplication `pagemtimes` Page-wise matrix multiplication (Da R2020b) `mpower` Matrix power `sqrtm` Matrix square root `expm` Matrix exponential `expmv` Matrix exponential multiplied by vector (Da R2023b) `logm` Matrix logarithm `funm` Evaluate general matrix function `kron` Kronecker tensor product `cross` Cross product `dot` Dot product
 `bandwidth` Lower and upper matrix bandwidth `tril` Lower triangular part of matrix `triu` Upper triangular part of matrix `isbanded` Determine if matrix is within specified bandwidth `isdiag` Determine if matrix is diagonal `ishermitian` Determine if matrix is Hermitian or skew-Hermitian `issymmetric` Determine if matrix is symmetric or skew-symmetric `istril` Determine if matrix is lower triangular `istriu` Determine if matrix is upper triangular
 `norm` Norme di vettori e di matrici `pagenorm` Page-wise matrix or vector norm (Da R2022b) `normest` 2-norm estimate `vecnorm` Vector-wise norm `cond` Condition number for inversion `condest` 1-norm condition number estimate `rcond` Reciprocal condition number `condeig` Condition number with respect to eigenvalues `det` Matrix determinant `null` Null space of matrix `orth` Orthonormal basis for range of matrix `rank` Rank of matrix `rref` Reduced row echelon form (Gauss-Jordan elimination) `trace` Sum of diagonal elements `subspace` Angle between two subspaces