# Kernel of a matrix

From Encyclopedia of Mathematics

A matrix of size over a field defines a linear function between the standard vector spaces and by the well-known formula

The kernel of the matrix is the kernel of the linear mapping . The kernel of (respectively, of ) is also called the null space or nullspace of (respectively, ).

#### References

[a1] | G. Strang, "Linear algebra and its applications" , Harcourt–Brace–Jovanovich (1988) pp. 92 |

[a2] | H. Schneider, G.P. Barker, "Matrices and linear algebra" , Dover, reprint (1989) pp. 215 |

[a3] | B. Noble, J.W. Daniel, "Applied linear algebra" , Prentice-Hall (1977) pp. 157 |

[a4] | Ch.G. Cullen, "Matrices and linear transformations" , Dover, reprint (1990) pp. 187 |

**How to Cite This Entry:**

Kernel of a matrix. M. Hazewinkel (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Kernel_of_a_matrix&oldid=12040

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098