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:
“On the 31st of August, 1846, I left Concord in Massachusetts for Bangor and the backwoods of Maine,... I proposed to make excursions to Mount Ktaadn, the second highest mountain in New England, about thirty miles distant, and to some of the lakes of the Penobscot, either alone or with such company as I might pick up there.”
—Henry David Thoreau (1817–1862)
“A strong person makes the law and custom null before his own will.”
—Ralph Waldo Emerson (1803–1882)
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—Alicia F. Lieberman (20th century)