L1_10 - ESI 6314 Deterministic Methods in Operations...

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Unformatted text preview: ESI 6314 Deterministic Methods in Operations Research Lecture Notes on Section 2 University of Florida Department of Industrial and Systems Engineering / REEF Matrices and Vectors Definitions Matrices Definition: m n matrix A = a 11 a 12 . .. a 1 n a 21 a 22 . .. a 2 n . . . . . . . . . . . . a m 1 a m 2 . .. a mn Example 1 2 3 4 1 2 6 3 4 7 1 3 1 3 Matrices and Vectors Definitions Matrices Definition: m n matrix A = a 11 a 12 . .. a 1 n a 21 a 22 . .. a 2 n . . . . . . . . . . . . a m 1 a m 2 . .. a mn Example 1 2 3 4 1 2 6 3 4 7 1 3 1 3 Matrices and Vectors Definitions Matrices Definition: Transpose of a matrix A = a 11 a 12 . .. a 1 n a 21 a 22 . .. a 2 n . . . . . . . . . . . . a m 1 a m 2 . .. a mn A T = a 11 a 21 . .. a m 1 a 12 a 22 . .. a n 2 . . . . . . . . . . . . a 1 n a 2 n . .. a mn Example A = 1 2 6 3 4 7 A T = 1 3 2 4 6 7 B = 1 3 B T = 1 3 Matrices and Vectors Definitions Matrices Definition: Transpose of a matrix A = a 11 a 12 . .. a 1 n a 21 a 22 . .. a 2 n . . . . . . . . . . . . a m 1 a m 2 . .. a mn A T = a 11 a 21 . .. a m 1 a 12 a 22 . .. a n 2 . . . . . . . . . . . . a 1 n a 2 n . .. a mn Example A = 1 2 6 3 4 7 A T = 1 3 2 4 6 7 B = 1 3 B T = 1 3 Matrices and Vectors Definitions Vectors Definition: a special type of matrix c = a 1 a 2 . . . a n c T = a 1 a 2 . .. a n Example 1 3 1 3 Matrices and Vectors Definitions Vectors Definition: a special type of matrix c = a 1 a 2 . . . a n c T = a 1 a 2 . .. a n Example 1 3 1 3 Matrices and Vectors Arithmetic Operations Addition of two matrices Definition: Both matrices should have the same size A + B = a 11 a 12 . .. a 1 n a 21 a 22 . .. a 2 n . . . . . . . . . . . . a m 1 a m 2 . .. a mn + b 11 b 12 . .. b 1 n b 21 b 22 . .. b 2 n . . . . . . . . . . . . b m 1 b m 2 . .. b mn = a 11 + b 11 a 12 + b 12 . .. a 1 n + b 1 n a 21 + b 21 a 22 + b 22 . .. a 2 n + b 2 n . . . . . . . . . . . . a m 1 + b m 1 a m 2 + b m 2 . .. a mn + b mn Matrices and Vectors Arithmetic Operations Addition of two matrices Example 1 2 6 3 4 7 + 4 7 9 3 10 5 = 5 9 15 6 14 12 Matrices and Vectors Arithmetic Operations Multiplication of a matrix by a scalar Definition: A = a 11 a 12 . .. a 1 n . . ....
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L1_10 - ESI 6314 Deterministic Methods in Operations...

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