Capa do livro de Schur Decomposition
Título do livro:

Schur Decomposition

Betascript Publishing (2010-11-12 )

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ISBN- 1 3:

978-613-1-15643-4

ISBN- 1 0:
6131156433
EAN:
9786131156434
Idioma do livro:
Inglês
Anotações e citações/ texto breve:
In the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is an important matrix decomposition. A constructive proof for the Schur decomposition is as follows: every operator A on a complex finite-dimensional vector space has an eigenvalue λ, corresponding to some eigenspace Vλ. Let Vλ⊥ be its orthogonal complement. It is clear that, with respect to this orthogonal decomposition, A has matrix representation (one can pick here any orthonormal bases spanning Vλ and Vλ⊥ respectively) A = begin{bmatrix} lambda , I_{lambda} & A_{12} 0 & A_{22} end{bmatrix}: begin{matrix} V_{lambda} oplus V_{lambda}^{perp} end{matrix} rightarrow begin{matrix} V_{lambda} oplus V_{lambda}^{perp} end{matrix} where Iλ is the identity operator on Vλ. The above matrix would be upper-triangular except for the A22 block. But exactly the same procedure can be applied to the sub-matrix A22, viewed as an operator on Vλ⊥, and its submatrices. Continue this way n times. Thus the space Cn will be exhausted and the procedure has yielded the desired result.
Editora:
Betascript Publishing
Website:
https://www.betascript-publishing.com/
Editado por:
Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
Número de páginas:
116
Publicado em:
2010-11-12
Stock:
Disponível
Categoria:
Matemática
Preço:
39 €
Palavras chave:
Mathematics, Linear Algebra, Issai Schur, Matrix Decomposition, Square Matrix, Complex Numbers

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