Fundamental theorem of linear algebra
In mathematics, the fundamental theorem of linear algebra is collection of statements regarding vector spaces and linear algebra, popularized by Gilbert Strang. The naming of these results is not universally accepted.
More precisely, let be a linear map between two finite-dimensional vector spaces, represented by a matrix of rank, then:
The transpose of is the matrix of the dual of. It follows that one has also:
- is the dimension of the row space of, which represents the image of ;
- is the dimension of the left null space of, which represents the kernel of ;
- is the dimension of the cokernel of.
The two first assertions are also called the rank–nullity theorem.
