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:
“We have left undone those things which we ought to have done; and we have done those things which we ought not to have done.”
—Morning Prayer, General Confession, Book of Common Prayer (1662)
“A strong person makes the law and custom null before his own will.”
—Ralph Waldo Emerson (1803–1882)
“Our passionate preoccupation with the sky, the stars, and a God somewhere in outer space is a homing impulse. We are drawn back to where we came from.”
—Eric Hoffer (1902–1983)