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:
“At the milliners, the ladies we met were so much dressed, that I should rather have imagined they were making visits than purchases. But what diverted me most was, that we were more frequently served by men than by women; and such men! so finical, so affected! they seemed to understand every part of a woman’s dress better than we do ourselves; and they recommended caps and ribbons with an air of so much importance, that I wished to ask them how long they had left off wearing them.”
—Frances Burney (1752–1840)
“A strong person makes the law and custom null before his own will.”
—Ralph Waldo Emerson (1803–1882)
“Why not a space flower? Why do we always expect metal ships?”
—W.D. Richter (b. 1945)