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:
“Nothing will be left white but here a birch,
And there a clump of houses with a church.”
—Robert Frost (1874–1963)
“A strong person makes the law and custom null before his own will.”
—Ralph Waldo Emerson (1803–1882)
“Though seas and land be ‘twixt us both,
Our faith and troth,
Like separated souls,
All time and space controls:
Above the highest sphere we meet
Unseen, unknown, and greet as angels greet.”
—Richard Lovelace (1618–1658)