The Wolfram Language provides several convenient methods for extracting and manipulating parts of matrices. The flexible [[ ]] (Part) and ;; (Span) syntaxes provide compact yet readable representations of operations on submatrices and matrix elements. The Wolfram Language's symbolic character also allows convenient pattern and rule-based element specifications.

Dimensions — dimensions of a matrix

MatrixQ — test whether an expression is a matrix

Part — elements and submatrices: m[[i,j]]; resettable with m[[i,j]]=x

Take — take rows, columns and submatrices

Drop — drop rows, columns and submatrices

Diagonal — get the list of elements on the diagonal

RotateLeft, RotateRight — cyclically rotate rows or columns

Reverse — reverse rows or columns

Transpose — interchange rows and columns

Join — join rows or columns of several matrices

UpperTriangularize  ▪  LowerTriangularize

Position — find positions where elements that match a pattern occur

Extract — extract elements that appear at a list of positions

ReplacePart — make replacements for collections of elements

ArrayRules — get a list of positions and values for nonzero elements

Map — apply a function at any level

MapApply —apply a function to the rows of a matrix

Symbolic Matrices

Indexed — represent a symbolically indexed matrix