«DIAGONALISABLE» 관련 영어 책
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1
Linear Algebra: Volume 2: An Introduction with Concurrent ...
The existence of such a list of eigenvectors is a necessary condition for the matrix
to be diagonalisable (but we shall not prove this). Consequently, the non-
existence of such a list of eigenvectors demonstrates that a matrix is not
diagonalisable ...
2
Basic Applied Mathematics For The Physical Sciences
(a) Not diagonalisable (b) Diagonalisable, P = (c) Not diagonalisable (d)
Diagonalisable P = 1 -1 -1 •1 10 1 0 1 , D = 1 0 0 0-2 0 |_0 0 -2J 8. A i i i 4 2 + V3
2 - V3 |_6 7 + 4V3 7 - 4V3 J ,D = k 0. A is not diagonalizable 9. (a) Diagonalisable
(b) ...
3
Basic Applied Mathemetics for the Physical Sciences
Strictly decreasing 17. Strictly decreasing 21. Strictly increasing 25. Answers to
Exercises. 1 -1 -1" -1 1 0 ,D = 1 0 1. 1 0 0" 0 -2 0 0 0 -2. 8. A = 0: * 0 , k * 0. A 9. (a)
Diagonalisable 1 (b) Diagonalisable (c) Not diagonalisable 10. Diagonalisable ...
4
Vectors, Pure and Applied: A General Introduction to Linear ...
E 6.4 Linear maps from (C2 to itself Theorem 6.3.3 gives a sufficient but not a
necessary condition for a linear map to be diagonalisable. The identity map L : IF"
—> IF" has only one eigenvalue but has the diagonal matrix I with respect to any
...
5
Basic Applied Mathematics for the Physical Sciences: Based ...
R. D. Sarma. 7. (a) Not diagonalisable l —l —-1 l 0 0, (b) Diagonalisable, P = —l l
0 , D = 0 —2 0 l 0 1 0 0 -2 (c) Not diagonalisable 1 1 1 4 0 0 (d)DiagonalisableP=
4 2+\/3 2-\/3 ,1)= 0 2+\/3 0 6 7 + 4\/3 7 - 4\/3 0 0 2 - \/3 8. A = 0: k[(l)], k ¢ 0.
6
Eigenvalues of Matrices: Revised Edition
1.6.1 Diagonalisable Matrices The matrix A is diagonalisable if and only if it is
similar to a diagonal matrix. Let D = diag(a1,...,a,,) be the diagonal matrix
consisting of the eigenvalues of A. Theorem 1.6.1 The matrix A is diagonalisable
if and ...
7
Mathematics for Economists: An Introductory Textbook
This result generalises: given a square matrix A which is not diagonalisable, we
can always find a d-matrix whose entries are arbitrarily close to those of A.
Actually we can go further, and say that "almost all square matrices are ...
Malcolm Pemberton, Nicholas Rau, 2001
8
Representations of Algebraic Groups
One may check that (8) c* = t o (A ® id) o A where t(fl <g> /2 ® /3) = /i<r(/3) ® /2-
2.5. (Diagonalisable Groups) Let A be a commutative group (written multi-
plicatively) ; identify A with the standard basis of the group algebra fc[A]. We
make KIA] ...
Jens Carsten Jantzen, 2007
9
Krylov Subspace Methods: Principles and Analysis
In [420, Corollary 2.5] it is shown that for a given matrix A there exists an HPD
matrix B such that A× is a rational function in A if and only if A is diagonalisable.
Moreover, it is shown that forAdiagonalisable the HPD matricesBfor whichA× is a
...
Jörg Liesen, Zdenek Strakos, 2012
10
Engineering Mathematics: Volume II
If G.M. and A.M. of an eigenvalue in respect of a square matrix A are equal then
we can find n linearly independent eigenvectors and hence A is diagonalisable.
Example 2.10 Prove that A "l f = i 0 1J is not diagonalisable. Solution The ...
