The left null space of a matrix A consists of all vectors x such that xTA = 0T, where T denotes the transpose of a column vector. The left null space of A is the same as the null space of AT. The left null space of A is the orthogonal complement to the column space of A, and is the cokernel of the associated linear transformation. The null space, the row space, the column space, and the left null space of A are the four fundamental subspaces associated to the matrix A.
Read more about this topic: Kernel (matrix)
Famous quotes containing the words left, null and/or space:
“The first month of his absence
I was numb and sick
And where he’d left his promise
Life did not turn or kick.
The seed, the seed of love was sick.”
—Alun Lewis (1915–1944)
“A strong person makes the law and custom null before his own will.”
—Ralph Waldo Emerson (1803–1882)
“There is commonly sufficient space about us. Our horizon is never quite at our elbows.”
—Henry David Thoreau (1817–1862)