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===Left null space===
The '''left null space''', or [[cokernel]], of a matrix {{mvar|A}} consists of all column vectors {{math|'''x'''}} such that {{math|1='''x'''<sup>T</sup>''A'' = '''0'''<sup>T</sup>}}, where T denotes the [[transpose]] of a matrix.  The left null space of {{mvar|A}} is the same as the kernel of {{math|''A''<sup>T</sup>}}. The left null space of {{mvar|A}} is the orthogonal complement to the [[column space]] of {{mvar|A}}, and is dual to the [[cokernel]] of the associated linear transformation. The kernel, the row space, the column space, and the left null space of {{mvar|A}} are the '''four fundamental subspaces''' associated with the matrix {{mvar|A}}.