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Matrix Operation (II)

Matrix Operation (II). ผศ.ดร.อนันต์ ผลเพิ่ม Anan Phonphoem http://www.cpe.ku.ac.th/~anan anan@cpe.ku.ac.th. Arithmetic Operation. Element-by-Element Matrix Operation. a 1 a 3 a 2 a 4. 2 1 0. b 1 b 3 b 2 b 4. A=. B=. A=. B=. 3 4 -1 5. 30 8 -1 0.

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Matrix Operation (II)

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  1. Matrix Operation (II) ผศ.ดร.อนันต์ ผลเพิ่ม Anan Phonphoem http://www.cpe.ku.ac.th/~anan anan@cpe.ku.ac.th

  2. Arithmetic Operation • Element-by-Element • Matrix Operation

  3. a1 a3 a2 a4 • 2 • 1 0 b1 b3 b2 b4 A= B= A= B= 3 4 -1 5 30 8 -1 0 (10)(3) (2)(4) (1)(-1) (0)(5) C= A.*B = C = A.*B (a1)(b1) (a3)(b3) (a2)(b2) (a4)(b4) = = Element-by-Element

  4. a1 a3 a2 a4 b1 b3 b2 b4 A= B= (a1)(b1)+(a3)(b2) (a1)(b3)+(a3)(b4) (a2)(b1)+(a4)(b2) (a2)(b3)+(a4)(b4) C = A*B = 10 2 1 0 • 4 • -1 5 A= B= • 50 • 3 4 (10)(3)+(2)(-1) (10)(4)+(2)(5) (1)(3)+(0)(-1) (1)(4)+(0)(5) C = A*B = = Matrix Operation

  5. x x x x y y X = Y = z z x x x x y y Matrix Multiplication (I) X * Y = 2 x 2 2 x 1 2 x 1

  6. x x x x x x y y X = Y = x x x x x x z z z y y Matrix Multiplication (II) X * Y = 3 x 1 3 x 2 2 x 1

  7. y y y y y y y y y y y y X = x x x x x x Y = z z Matrix Multiplication(III) X * Y = 1 x 2 1 x 3 3 x 2

  8. y y y y y y y y y y y y x x x x x x x x X = Y = z z z zz z Matrix Multiplication(IV) X * Y = 2 x 3 2 x 2 2 x 3

  9. x x x x x x X = y y y y y y Y = z z z zz z z z z Matrix Multiplication(V) X * Y = 3 x 3 3 x 1 1 x 3

  10. y y y y y y X = x x x x x x Y = z Matrix Multiplication(VI) X * Y = 1 x 1 1 x 3 3 x 1

  11. x x x x x x y y y y X = Y = x x x x x x Matrix Multiplication (VII) X * Y = Error Message 3 x 2 1 x 2

  12. y y y y y y z z z x x x x x x X = Y = X .* Y = Matrix Multiplication (VIII) X * Y = Error Message 1 x 3 1 x 3

  13. Special Matrix

  14. eye(3) = 0 0 00 1 0 0 01 0 0 0 1 1 1 1 11 1 1 1 1 ones(3) = zeros(2) = zeros(1,3) = 0 0 0 Special Matrix

  15. Zero Matrix I = 1 0 0 01 0 0 0 1 0 0 0 00 0 0 0 0 Special Matrix 0 A = A 0 = 0 I A = A I = A

  16. Order = 2 Order = 3 Polynomial f(x) = a1xn + a2xn-1 + a3xn-2 + …+ anx + an+1 n Degree = Order = Example: y = 3x2 + 4 y = 12x3 + 2x2 + 1

  17. Polynomial Coefficient f(x) = a1xn + a2xn-1 + a3xn-2 + …+ anx + an+1 [ a1 a2 a3… an-1 an an+1 ] y = 12x3 + 2x2 + 1 [ 12 2 0 1 ]

  18. y = 5x4 + 6x3 + 3x2 + 2 b = 4a3– 6a2 T = x3 + x2 + x + 1 Polynomial Coefficient [ 5 6 3 0 2 ] [ 4 -6 0 0 ] [ 1 1 1 1 ]

  19. Roots of y 1 , 2 Roots of polynomial a = [ 1 -3 2] y = x2– 3x+ 2 = (x – 1) (x– 2) c = roots(a) = [ 1 2 ] T = roots( [ 1 -3 2 ] )

  20. Polynomial of roots r = [ 1 2 ] Roots of y = 1 , 2 >>poly(r) ans = 1 -3 2 (x – 1) (x– 2) P = poly([ 1 2 ]) y = x2– 3x+ 2

  21. roots ( [1 –3 2 ] ) poly ( [1 2 ] ) Poly ( ) roots ( ) y = x2– 3x+ 2 [ 1 2 ] [ 1 –3 2 ] (x – 1)(x – 2)

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