# invariant subspace

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## invariant subspace

[in‚ver·ē·ənt ′səb‚spās]
(mathematics)
For a bounded operator on a Banach space, a closed linear subspace of the Banach space such that the operator takes any point in the subspace to another point in the subspace.
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References in periodicals archive ?
M = I) and do not consider restarting, we can analyze performance based on invariant subspace approximation.
The main theme of the proceedings is the invariant subspace of the shift operator S or its adjoint S*, on certain reproducing kernal Hilbert spaces of analytic functions on the open unit disk.
v) If M is an invariant subspace of T, then the restriction has [T|.
A subspace M is invariant for T if T(M) [subset not equal to] M and a part of an operator is a restriction of it to an invariant subspace.
Let X be the 3rd order B-spline shift invariant subspace.
We prove in such a case that these point bifurcations which are transversal to the invariant subspace generate two periodic of period 2 points in a neighbourhood of the given point and besides can simultaneously give rise to orbits that are homoclinic to the periodic points.
Suppose that in a locally convex space X there exists T [member of] L(X) which has no closed invariant subspace.
SRRIT is a Fortran program to calculate an approximate orthonormal basis for a dominant invariant subspace of a real matrix A by the method of simultaneous iteration.
A subspace M of X is an invariant subspace for T, if TM [subset or equal to] M; if further, dimX/M < [infinity], it is called a finite codimensional invariant subspace for T.
In case H is not unreduced, one has found an invariant subspace, often referred to as a lucky breakdown as the projected counterpart contains now all the essential information and one can solve the problem without approximation error; the residual becomes zero.
MATHEMATICAL EXPRESSION OMITTED] This invariant subspace has dimension 3.

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