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In [[control theory]], a '''controlled invariant subspace''' of the [[state space representation]] of some system is a [[Euc A subspace ''V'' ⊂ '''R'''^''n'' is a ''controlled invariant subspace'' if, for any '''x'''(0) ∈ ''V'', there is an input '''u'''(' ...

...can mathematician [[Victor Lomonosov]].<ref>{{cite journal|title=Invariant subspaces for the family of operators which commute with a completely continuous oper ==Lomonosov's invariant subspace theorem == ...

...h>V</math> is the union of a family of finite-dimensional <math>f</math>-[[invariant subspace]]s.<ref>{{cite arXiv|title=Central Simple Poisson Algebras|author1 ...r words, there exists a family <math>\{ V_i\vert i\in I\}</math> of linear subspaces of <math>V</math>, such that we have the following: ...

...mbly map is a [[Universal property|universal]] approximation of a homotopy invariant [[functor]] by a [[homology theory]] from the left. From the geometric view ...py equivalences). This reflects the fact that <math>h_*</math> is homotopy-invariant. ...

...ors|eigenvalue]] of an operator (or, more generally, a projector onto an [[invariant subspace]] corresponding to an isolated part of the spectrum). It was intro ...math>\mathfrak{L}_\Gamma</math> and <math>\mathfrak{N}_\Gamma</math> are [[invariant subspace]]s of the operator <math>A</math>. ...

In [[mathematics]] [[invariant theory]], the '''bracket ring''' is the [[subring]] of the [[Ring (mathemat ...ann variety whose points correspond to ''d''-dimensional [[Linear subspace|subspaces]] of an ''n''-dimensional space.<ref>Sturmfels (2008) pp.78–79</ref> ...

...ce. If the flats do not intersect, their shortest [[distance]] is one more invariant.<ref name= "jordan"/> These angles are called '''canonical'''<ref name="afr ...over the complex numbers. (For [[#Angles between subspaces|angles between subspaces]], the generalization to <math>\mathbb C^n</math> is discussed by Galántai ...

...A</math>-module <math>M</math> is a [[topology]] on <math>M</math> that is invariant under translations and admits a fundamental system of neighborhood of <math ...aring in functional analysis are typically not linearly topologized (since subspaces do not form a neighborhood system). ...

..., for irreducible representations of C*-algebras, the only non-zero linear invariant subspace is the whole space. ...<math>\{0\}</math> and <math>\mathcal{H}</math> are the only closed stable subspaces under <math>\mathcal{F}</math>. The family <math>\mathcal{F}</math> is said ...

In some cases, a slow manifold is defined to be the invariant manifold on which the dynamics are slow compared to the dynamics off the ma ...nter manifold]] three of the subspaces are the stable, unstable and center subspaces corresponding to the span of the eigenvectors with eigenvalues <math>\lambd ...

...tt ring (forms)|Witt ring]] of the ternary forms attached to the imaginary subspaces of ''A'' and ''B''.<ref>{{cite book | last=Knus | first=Max-Albert | title= A nonreal linked field has [[u-invariant]] equal to 1,2,4 or 8.<ref name=Lam/>{{rp|406}} ...

...al vector space) is said to be ''simple'' if its only [[invariant subspace|invariant]] [[linear subspace]]s under ''T'' are {0} and ''V''. If the field is [[Alg ...]]s), the simple vector spaces are those that contain no proper nontrivial subspaces. Therefore, the one-[[dimension (linear algebra)|dimensional]] vector space ...

...rst1=Shobhit |last2=Haller |first2=George |year=2022 |title=How to compute invariant manifolds and their reduced dynamics in high-dimensional finite element mod ...016-2974-z |s2cid=44074026}}</ref> SSM theory provides conditions for when invariant properties of eigenspaces of a linear dynamical system can be extended to a ...

{{Short description|Subspace of a quantum system's Hilbert space that is invariant to non-unitary dynamics}} ...that (possibly) won't require any ''active'' stabilization methods. These subspaces prevent destructive environmental interactions by isolating [[quantum infor ...

Procesi studies noncommutative algebra, algebraic groups, invariant theory, enumerative geometry, infinite dimensional algebras and quantum gro arrangements of subspaces and tori. ...

...al [[Hilbert space]] and Calkin sequence spaces (also called rearrangement invariant sequence spaces). The correspondence is implemented by mapping an operator ...–ket notation]] has been used for the one-dimensional projections onto the subspaces spanned by individual basis vectors. The sequence of absolute values of the ...

...partite [[quantum state]] density matrix that is [[Invariant (mathematics)|invariant]] under all [[unitary operator]]s of the form <math>U \otimes U</math>. Tha ...jection (linear algebra)|projectors]] onto the symmetric and antisymmetric subspaces, with the relative weight <math>p \in [0,1]</math> being the main parameter ...

...[[convex cone]] in a [[Lie algebra]] of a connected [[Lie group]] that is invariant under [[inner automorphism]]s. The study of such cones was initiated by [[E ...topology)|interior]] of the cone intersects the interior of the Weyl group invariant cone. ...

...clusions on the system's [[Reachability problem|reachable]] and observable subspaces. ...

...-integrable function]]s on the Heisenberg manifold has a right-translation-invariant orthogonal decomposition: ...ath> can further be decomposed into right-translation-invariant orthogonal subspaces ...