Kernel of a linear operator
From Encyclopedia of Mathematics
The linear subspace of the domain of definition of a linear operator that consists of all vectors that are mapped to zero.
The kernel of a continuous linear operator that is defined on a topological vector space is a closed linear subspace of this space. For locally convex spaces, a continuous linear operator has a null kernel (that is, it is a one-to-one mapping of the domain onto the range) if and only if the adjoint operator has a weakly-dense range.
The nullity is the dimension of the kernel.
References
| [a1] | J.L. Kelley, I. Namioka, "Linear topological spaces", v. Nostrand (1963) pp. Chapt. 5, Sect. 21 |
How to Cite This Entry:
Kernel of a linear operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Kernel_of_a_linear_operator&oldid=53878
Kernel of a linear operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Kernel_of_a_linear_operator&oldid=53878
This article was adapted from an original article by G.L. Litvinov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article