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Matrix

Defines Matrix, matrix

A matrix is a rectangular array of scalars from a field FF, arranged in rows and columns. An m×nm \times n matrix has mm rows and nn columns.

Every linear map between finite-dimensional vector spaces can be represented by a matrix, once bases are chosen. Matrix multiplication corresponds to composition of linear maps. The set of n×nn \times n matrices over FF forms a (generally non-commutative) ring.

A square matrix is invertible if and only if its determinant is nonzero, equivalently if the corresponding linear map is bijective.

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@misc{emsenn2026-matrix,
  author    = {emsenn},
  title     = {Matrix},
  year      = {2026},
  url       = {https://emsenn.net/library/math/domains/linear-algebra/terms/matrix/},
  publisher = {emsenn.net},
  license   = {CC BY-SA 4.0}
}