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 must remember the past, define the future, and challenge the present—wherever and however we can. It will take the rest of our lives even to begin. But then, what else have we to do?”
—Jane O’Reilly, U.S. feminist and humorist. The Girl I Left Behind, Introduction (1980)
“A strong person makes the law and custom null before his own will.”
—Ralph Waldo Emerson (1803–1882)
“It is the space inside that gives the drum its sound.”
—Hawaiian saying no. 1189, ‘lelo No’Eau, collected, translated, and annotated by Mary Kawena Pukui, Bishop Museum Press, Hawaii (1983)