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6.6 Column space, row space, and rank
Read a matrix as both a source of outputs and a source of linear relations, then use rank to count the genuinely independent directions that remain.
Course contents
MATH1030: Linear algebra I
Linear algebra notes.
3.13.1 Matrix multiplication and identity matrices3.23.2 Transpose and special matrices3.33.3 Row-operation matrices3.13.1 Matrix addition, subtraction, and scalar multiplication3.23.2 Matrix multiplication and linear systems3.33.3 Transposes, symmetric matrices, and skew-symmetric matrices3.43.4 Special matrices3.53.5 Block matrices
6.16.1 Vector spacesMember6.26.2 SubspacesMember6.36.3 Linear combinations and spanMember6.46.4 Linear dependence and independenceMember6.56.5 Basis and dimensionMember6.66.6 Column space, row space, and rankCurrent sectionMember6.76.7 Matrix subspaces, basis, and dimensionMember6.86.8 Basis extension and change of basisMember
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