A1Bn mXn nXnnn XX n - n! n (Vandermonde) () () 1 A=A 2 () 3 () 4 () 5 ()0 6 ()0 5+3 7 ()00 8 ()k() n NN N? ?.mmap - 2009-11-7 - mn ? =0 =0 :A+B=B+A :A+(B+C)=(A+B)+C AA+0=0+A=A A-AA+(-A)=0 klAB 1A=A,0A=0 k(lA)=(kl)A k(A+B)=kA+kB (k+l)A=kA+lA n A(BC)=(AB)C (A+B)C=AC+BC C(A+B)=CA+CB k(kA)B=A(kB) 0 AB ABE (E+A)(E+A)=E*exp(2)+2A+A*exp(2) Ak*Al =0 AXA=0?|A|X|A|=0|A|=0 |A|=0 ad-bc=0?a/b=c/d k EnE A AkA k=Xn-1 A =1 X A An nB AB=BA=E A BA 0 A*XA=|A|XE ABA+B nA A AX=B XA=B X A A,B ?.mmap - 2009-11-7 - += ij (ij) i(i) 1/ ikj (jki) ikj ?= BAAB ABBA ABBCAC r 0 A AB=BA=E |A|0 AmXn mn r(A)=m n 0 k1=k2=.=ks=0 n n 0 XOY (1)(2) 12 (1)(2) AB - - (RREF) 1 00 RREF ? .mmap - 2009-11-9 - n m m,n 0b=0 0?0 m=n Cramer Ax=b = 1 bA r(A)=n r(A)n bA + Ax=b A An mn Amxn RREFrn-r n-r n-r Ax=0 = = 823 2122 ?.mmap - 2009-11-11 - n n n+1 rV nn n+1 1 23 4 =1 A=1 =0 |A|=1 |A|=-1 ?.mmap - 2009-11-12 -