combinepdf-min-0293.pdf

# combinepdf-min-0293.pdf - Notes on linear algebra(Monday...

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Unformatted text preview: Notes on linear algebra (Monday 17th October, 2016, 23:10) page 140 Proposition 3.114. Let n E N. Then, there are precisely a! permutation matrices of size a x :1. (Recall that a! denotes the number 1 - 2 - 3 ----- a; it is called the “factorial of a”. For instance, 5! = 1 -2 - 3 - 4 - 5 : 120.) We will outline a proof of Proposition 3.114 in Section 3.21. Example 3.115. Proposition 3.114 (applied to n = 3) says that there are precisely 3! = 6 permutation matrices of size 3 X 3. Here are they: 1 13:0 0 0 TLBZO 1 0 1 010 A21 OIf 3:001. 010 100 The two last matrices, which I have here denoted by A and B, are neither the CDC} GHQ GHQ CDCJH \_______/ 5'] Lu || /""—"‘\ ...
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