MATA23H3 Lecture Notes - Lecture 5: Scalar Multiplication, Main Diagonal, The Young Turks
Document Summary
Mata23 - lecture 5 - properties of matrix operations. Matrix symmetry continued: example 5: let matrix a = [aij] mn,n(r). Show that a + at is symmetric. n n. A + at = [aij + aji]n n. = [a + at ]t = [aji + aij]n n. 3 4 (cid:21) (cid:20) 1 2 (cid:21) (cid:21) (cid:20)0 0 (cid:20) 1 2. R((cid:126)u (cid:126)v) = (r(cid:126)u)(cid:126)v = (cid:126)u (r(cid:126)v: r(ab) = (ra)b = a(rb) R(ab)ij = r(ith row of a) (jth column of b) R(a)bij = [r(ith row of a)] (jth column of b) A(rb)ij = (ith row of a) [r(jth column of b): multiplication: let a, b, c be matrices such that all the following are de ned. (also note. Am n, bn k, ck r: a(bc) = (ab)c, a(b + c) = ab + ac. A(b + c)ij = (ith row of a) (jth column of b + c)
