Kernel of a matrix

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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, ).


[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:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098