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Matrices and Linear Algebra—Wolfram Language Documentation

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• Functions
  • ArrayRules
  • CholeskyDecomposition
  • CoefficientArrays
  • Cross
  • Det
  • Diagonal
  • DiagonalMatrix
  • DiagonalMatrixQ
  • Dimensions
  • Dot
  • Drop
  • Eigenvalues
  • HilbertMatrix
  • IdentityMatrix
  • Inverse
  • KarhunenLoeveDecomposition
  • LeastSquares
  • LinearSolve
  • LUDecomposition
  • MatrixExp
  • MatrixForm
  • MatrixPlot
  • MatrixPropertyDistribution
  • MatrixQ
  • MatrixRank
  • Minors
  • Norm
  • Normal
  • Normalize
  • NullSpace
  • Orthogonalize
  • Part
  • Position
  • PositiveDefiniteMatrixQ
  • PrincipalComponents
  • Projection
  • PseudoInverse
  • QRDecomposition
  • RandomVariate
  • RotationMatrix
  • RowReduce
  • SchurDecomposition
  • SingularValueDecomposition
  • SparseArray
  • SymmetricMatrixQ
  • Table
  • Take
  • Total
  • Tr
  • Transpose
  • UpperTriangularize
  • UpperTriangularMatrixQ
  • WishartMatrixDistribution
• Related Guides
  • Sparse Arrays
  • Structured Arrays
  • Symbolic Arrays
  • Tensors
  • Geometric Transformations
  • Basic Linear Algebra Subroutines - BLAS
  • Equation Solving
  • Image Processing
  • Fourier Analysis
  • Wavelet Analysis
  • Random Matrices
• Tech Notes
  • Vectors and Matrices
  • Vector Operations
  • Constructing Matrices
  • Basic Matrix Operations
  • Solving Linear Systems
  • Eigenvalues and Eigenvectors
  • Advanced Matrix Operations
  • Sparse Arrays: Linear Algebra
  • Constrained Optimization

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.

+, *, ^, ... — automatically operate element-wise: {a,b}+{c,d}->{a+c,b+d}

Dot (.) — scalar dot product

Cross  ▪  Norm  ▪  Total  ▪  Normalize  ▪  Projection  ▪  Orthogonalize  ▪  ...

Table — construct a matrix from an expression

IdentityMatrix  ▪  DiagonalMatrix  ▪  RotationMatrix  ▪  HilbertMatrix  ▪  ...

Part — a part or submatrix: m[[i,j]]; resettable with m[[i,j]]=x

Dimensions  ▪  Take  ▪  Drop  ▪  Diagonal  ▪  Position  ▪  UpperTriangularize  ▪  ...

Dot(.)  ▪  Inverse  ▪  Transpose  ▪  Det  ▪  Tr  ▪  Eigenvalues  ▪  MatrixExp  ▪  ...

LinearSolve  ▪  NullSpace  ▪  MatrixRank  ▪  RowReduce  ▪  Minors  ▪  ...

LeastSquares  ▪  PseudoInverse  ▪  Norm  ▪  ...

SingularValueDecomposition  ▪  QRDecomposition  ▪  LUDecomposition  ▪  CholeskyDecomposition  ▪  SchurDecomposition  ▪  ...

PrincipalComponents  ▪  KarhunenLoeveDecomposition  ▪  ...

MatrixQ  ▪  DiagonalMatrixQ  ▪  UpperTriangularMatrixQ  ▪  SymmetricMatrixQ  ▪  PositiveDefiniteMatrixQ  ▪  ...

RandomVariate  ▪  WishartMatrixDistribution  ▪  MatrixPropertyDistribution  ▪  ...

MatrixForm — display a matrix in 2D form

MatrixPlot — visualize a matrix using colors for elements

SparseArray — construct a sparse matrix from positions and values

ArrayRules  ▪  Normal  ▪  CoefficientArrays  ▪  ...

"CSV"  ▪  "HDF5"  ▪  "HDF"  ▪  "MAT"  ▪  "MTX"  ▪  "HarwellBoeing"  ▪  ...

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