Given two sets of m vectors, x; R and y; ER for all i = 1,2,,m,...

 

Transcribed Image Text:

Given two sets of m vectors, x; R" and y; ER" for all i = 1,2,,m, verify that the summations 1xx and xy can be vectorized as the following matrix multiplications: where X = [x1 x2 Your answers: m m Exy=x XX = XX and [xy] =XY, i=1 == i=1 Xm] RX and Y = [y1 y2 ym] R"*m. Exercise 2 (10 marks) Q2.5 on page 64. For any matrix AER"x", if we use a; (i = 1,2,...,n) to denote the ith column of the matrix A and use gij = | cos bij = |a; a;\/(||a;||||aj||) to denote the absolute cosine of the angle 0;; between any two vectors a; and a; (for all 1 Given two sets of m vectors, x; R" and y; ER" for all i = 1,2,,m, verify that the summations 1xx and xy can be vectorized as the following matrix multiplications: where X = [x1 x2 Your answers: m m Exy=x XX = XX and [xy] =XY, i=1 == i=1 Xm] RX and Y = [y1 y2 ym] R"*m. Exercise 2 (10 marks) Q2.5 on page 64. For any matrix AER"x", if we use a; (i = 1,2,...,n) to denote the ith column of the matrix A and use gij = | cos bij = |a; a;\/(||a;||||aj||) to denote the absolute cosine of the angle 0;; between any two vectors a; and a; (for all 1