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 violence and obscenity are left unadulterated, as manifestation of the mystery and pain which ever accompanies the act of creation.”
—Anaïs Nin (1903–1977)
“A strong person makes the law and custom null before his own will.”
—Ralph Waldo Emerson (1803–1882)
“Here in the U.S., culture is not that delicious panacea which we Europeans consume in a sacramental mental space and which has its own special columns in the newspapers—and in people’s minds. Culture is space, speed, cinema, technology. This culture is authentic, if anything can be said to be authentic.”
—Jean Baudrillard (b. 1929)