Invariant Subspaces of Matrices with ApplicationsThis unique book addresses advanced linear algebra from a perspective in which invariant subspaces are the central notion and main tool. It contains comprehensive coverage of geometrical, algebraic, topological, and analytic properties of invariant subspaces. The text lays clear mathematical foundations for linear systems theory and contains a thorough treatment of analytic perturbation theory for matrix functions. |
Contents
CL51_introduction | 2 |
CL51_pt1 | 4 |
CL51_ch1 | 5 |
CL51_ch2 | 45 |
CL51_ch3 | 105 |
CL51_ch4 | 121 |
CL51_ch5 | 144 |
CL51_ch6 | 189 |
CL51_ch12 | 359 |
CL51_pt3 | 385 |
CL51_ch13 | 387 |
CL51_ch14 | 423 |
CL51_ch15 | 444 |
CL51_ch16 | 482 |
CL51_ch17 | 514 |
CL51_pt4 | 563 |
CL51_ch7 | 212 |
CL51_ch8 | 262 |
CL51_pt2 | 293 |
CL51_ch9 | 295 |
CL51_ch10 | 316 |
CL51_ch11 | 339 |
CL51_ch18 | 565 |
CL51_ch19 | 604 |
CL51_ch20 | 624 |
CL51_appendixa | 646 |
CL51_backmatter | 679 |
Other editions - View all
Invariant Subspaces of Matrices with Applications Israel Gohberg,Peter Lancaster,Leiba Rodman Limited preview - 1986 |
Invariant Subspaces of Matrices With Applications I. Gohberg,P. Lancaster,L. Rodman Snippet view - 1986 |
Common terms and phrases
A-invariant A₁ A₂ algebra analytic family assume B₁ B₂ block matrix C₁ coinvariant companion matrix complex numbers Corollary corresponding defined denote diagonal direct complement direct sum distinct eigenvalues easily seen eigenvalue eigenvector equation example exists f₁ family of subspaces finite follows formula Hence implies inequality Inv(A Inv(B invariant subspaces irreducible subspace Jordan basis Jordan block Jordan chain Jordan form Jordan structure k₁ Ker(A kernel pair L₁ L₂ lattice Lemma linear system linear transformation linearly independent Lipschitz stable M₁ M₂ minimal factorization minimal realization monic matrix polynomial N₁ neighbourhood nonzero obtain one-dimensional orthogonal orthonormal basis P₁ partial multiplicities projector proof of Theorem Proposition prove rational matrix functions resp respect root subspaces S₁ S₂ scalar Section semiinvariant sequence shows solution Span{e spectral standard triple Theorem triinvariant decomposition upper triangular V₁ x₁ Y₁ zero λο