▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Map
▾ Operation
▾ N-operation
▾ Binary operation
▾ Enclosed binary operation
▾ Groupoid
▾ Ringoid
▾ Semiring
▾ Ring
▾ Left ring action
▾ Module
▾ Vector space
▾ Vector subspace
▾ Linear span
▾ Euclidean complex linear span
▾ Complex matrix column space
▾ Complex matrix standard column space
▾ Complex matrix rank
Full rank complex matrix
Formulation 0
Let $A \in \mathbb{C}^{N \times M}$ be a D999: Complex matrix.
Then $A$ is a full rank complex matrix if and only if \begin{equation} \text{rank} A = \min(N, M) \end{equation}