Matrices and Linear Algebra

Mathematica automatically handles both numeric and symbolic matrices, seamlessly switching among large numbers of highly-optimized algorithms. Using many original methods, Mathematica can handle numerical matrices of any precision, automatically invoking machine-optimized code when appropriate. Mathematica 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+b,c+d}

Dot (.) — scalar dot product

Constructing Matrices »

Table — construct a matrix from an expression

Parts of Matrices »

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

Matrix Operations »

Linear Systems »

Minimization Problems »

Matrix Decompositions »

Matrix Tests

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

Data Formats