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:
“Simplicity is an acquired taste. Mankind, left free, instinctively complicates life.”
—Katharine Fullerton Gerould (1879–1944)
“A strong person makes the law and custom null before his own will.”
—Ralph Waldo Emerson (1803–1882)
“For good teaching rests neither in accumulating a shelfful of knowledge nor in developing a repertoire of skills. In the end, good teaching lies in a willingness to attend and care for what happens in our students, ourselves, and the space between us. Good teaching is a certain kind of stance, I think. It is a stance of receptivity, of attunement, of listening.”
—Laurent A. Daloz (20th century)