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:
“He had forty-two boxes, all carefully packed,
With his name painted clearly on each:
But, since he omitted to mention the fact,
They were all left behind on the beach.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“A strong person makes the law and custom null before his own will.”
—Ralph Waldo Emerson (1803–1882)
“Stars scribble on our eyes the frosty sagas,
The gleaming cantos of unvanquished space . . .”
—Hart Crane (1899–1932)