Matrices and Linear Algebra
The Wolfram Language automatically handles both numeric and symbolic matrices, seamlessly switching among large numbers of highly optimized algorithms. Using many original methods, the Wolfram Language can handle numerical matrices of any precision, automatically invoking machine-optimized code when appropriate. The Wolfram Language handles both dense and sparse matrices and can routinely operate on matrices with millions of entries.
Operations on Vectors »
+ , * , ^ , ... — automatically operate element-wise: {a,b}+{c,d}->{a+c,b+d}
Cross ▪ Norm ▪ Total ▪ Normalize ▪ Projection ▪ Orthogonalize ▪ ...
Constructing Matrices »
Table — construct a matrix from an expression
IdentityMatrix ▪ DiagonalMatrix ▪ RotationMatrix ▪ HilbertMatrix ▪ ...
Parts of Matrices »
Part — a part or submatrix: m[[i,j]]; resettable with m[[i,j]]=x
Dimensions ▪ Take ▪ Drop ▪ Diagonal ▪ Position ▪ UpperTriangularize ▪ ...
Matrix Operations »
Dot (. ) ▪ Inverse ▪ Transpose ▪ Det ▪ Tr ▪ Eigenvalues ▪ MatrixExp ▪ ...
Linear Systems »
LinearSolve ▪ NullSpace ▪ MatrixRank ▪ RowReduce ▪ Minors ▪ ...
Minimization Problems »
LeastSquares ▪ PseudoInverse ▪ Norm ▪ ...
Matrix Decompositions »
SingularValueDecomposition ▪ QRDecomposition ▪ LUDecomposition ▪ CholeskyDecomposition ▪ SchurDecomposition ▪ ...
PrincipalComponents ▪ KarhunenLoeveDecomposition ▪ ...
Matrix Predicates »
MatrixQ ▪ DiagonalMatrixQ ▪ UpperTriangularMatrixQ ▪ SymmetricMatrixQ ▪ PositiveDefiniteMatrixQ ▪ ...
Random Matrices »
RandomVariate ▪ WishartMatrixDistribution ▪ MatrixPropertyDistribution ▪ ...
Displaying Matrices
MatrixForm — display a matrix in 2D form
MatrixPlot — visualize a matrix using colors for elements
Sparse Arrays »
SparseArray — construct a sparse matrix from positions and values
ArrayRules ▪ Normal ▪ CoefficientArrays ▪ ...
Data Formats »
"CSV" ▪ "HDF5" ▪ "HDF" ▪ "MAT" ▪ "MTX" ▪ "HarwellBoeing" ▪ ...