พีชคณิต

hJol~n~

1. F)J~@dl 2.

A th symmetric U&9 A’ Odh symmetric dhU

ni A tilutu~fn&@%

5GpZ7

(1) AA’ LW A’A t&.4 symmetric (2) A + A’ LOU symmetric (3) A-A’ th skew - symmetric 3. IhJoli’n~ A LW B th symmetric WGigT~tiil (1) A + B t6U symmetric (2) AB l&t symmetric l%ltdO AB = BA 4. P~t!hMJol~n~

A \%$UJLhWlJXlllO~

symmetric matrix LLR: skew-symmetric

matrix t&I 3-2 5

A = I

-1

1 2

3

6

2

I

(1)

(CA)* = EA*

(2)

A = x

(3)

(A)’

(4)

(A*)* = A

(6)

iiii

=

A’

( 5 ) (A+B)* = A * + B *

=

iiE

( 7 ) (AB)’ = B*A*

6. #I A t%.WJ~‘rfdhl

7 %$$a7 A*A LLA: AA* th Hermitian

7. fhJol?n~ H dU Hermitian PJ$fil~~l

B*HB Il:th Hermitian &Xl

8. ~~~~~d~lR~l~n~~~‘lUtt~~t~~~tt~J~~~oJ 9 . 51 A tilUtuAna’Cq?~~J

A = -A* (iiU&~

Hermitian matrix thIh?UO?J aij = -3 t~icxiuntu~3nB

A +h

skew Hermitian PJw^~d+h (1) iA ti)U skew-Hermitian $1 A th Hermitian (2) iA th Hermitian 51 A tfh4 skew-Hermitian

34

MA

226