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Parts of Matrices
Mathematica 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. Mathematica'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
    
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
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