Fundamental theorem of linear algebra

In mathematics, the fundamental theorem of linear algebra makes several statements regarding vector spaces. Those statements may be given concretely in terms of the rank r of an m × n matrix A and its singular value decomposition: In mathematics, the fundamental theorem of linear algebra makes several statements regarding vector spaces. Those statements may be given concretely in terms of the rank r of an m × n matrix A and its singular value decomposition: First, each matrix A ∈ R m × n {displaystyle Ain mathbb {R} ^{m imes n}} ( A {displaystyle A} has m {displaystyle m} rows and n {displaystyle n} columns) induces four fundamental subspaces. These fundamental subspaces are as follows: