1.1 Special Form Matrices o Basic matrices:defined by the outer product of an m x 1 basic vector and an n x 1 basic vector: xn)em(e7 Properties: ()写mxx=Emx (2)(E写x)T=Exm网 m n )4=盆 amx列 (4)E$xmAX”=aEX (5)det(x=0, (m=n>1) 1 Special Matrices 5/601.1 Special Form Matrices Basic matrices: defined by the outer product of an m × 1 basic vector and an n × 1 basic vector: E (m×n) ij = e (m) i (e (n) j ) T . Properties: (1) E (m×n) ij E (n×r) kl = δjkE (m×r) il (2) (E (m×n) ij ) T = E (n×m) ji (3) A = Pm i=1 Pn j=1 aijE (m×n) ij (4) E (s×m) ij AE(n×r) kl = ajkE (s×r) il (5) det(E (m×n) ij ) = 0, (m = n > 1) 1 Special Matrices 5 / 60