[過去ﾛｸﾞ] 純粋・応用数学・数学隣接分野（含むガロア理論）19 (1002ﾚｽ)
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734(1): 04/04(金)07:58 ID:CsC7EptL(2/3) AAS
つづき

外部ﾘﾝｸ:en.wikipedia.org
Commuting matrices

Characterizations and properties
・Two diagonalizable matrices
A and B commute ( AB=BA if they are simultaneously diagonalizable (that is, there exists an invertible matrix
P such that both P^{-1}AP and P^{-1}BP are diagonal).[4]: p. 64 
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739(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 04/04(金)10:26 ID:nFnX0O4C(1/4) AAS
>>734 補足
>4 Horn, Roger A.; Johnson, Charles R. (2013). Matrix Analysis, second edition. Cambridge University Press. ISBN 9780521839402.

これの海賊版PDFが見つかった
P62
Theorem 1.3.12. Let A, B ∈ Mn be diagonalizable. Then A and B commute if and only if they are simultaneously diagonalizable.
Proof.
Assume that A and B commute, perform a similarity transformation on both A and B that diagonalizes A (but not necessarily B) and groups together any repeated eigenvalues of A. Ifμ1,...,μd are the distinct eigenvalues of A and n1,...,nd are their respective multiplicities, then we may assume that
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