2130_Chapter7_Notes

ia 0 0 1 a for any n n matrix a just as the

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Unformatted text preview: ne vectors ai then cij ai1 ai2 ¤¤¤ ain and bj b1j b2j ¤¤¤ bnj , ai ¤ bj , the dot product of the ith row of A with the j th column of B. 11 / 17 6 Examples A 12 , 34 12 21 B AB and Note: AB BA 12 34 12 21 1 4 2 2 3 8 6 4 54 , 11 10 BA 12 21 12 34 1 6 2 8 2 3 4 4 7 10 . 58 matrix multiplication is not commutative. 12 / 17 Identity Matrix The multiplicative identity matrix I is an n ¢ n matrix with 1 in each diagonal entry and 0 in all other entries: I 10 01 .. .. .. 00 The identity matrix I is analogous to the number 1 : AI r ¤ 1 1 ¤ r r for any real number r. ¤¤¤ ¤¤¤ .. . ¤¤¤ IA 0 0 .. . . 1 A for any n ¢ n matrix A, just as The dimensions of I depend on the context. Both of the matrices below are identity matrices: I 10 , 01 I 100 010. 001 13 / 17 7 Inverse Matrix A square matrix A is nonsingular, or invertible, if there exists a matrix B such that AB A is singular. BA I. Otherwise, The matrix B, if it exists, is unique. It is denoted by A¡1 and is called the inverse of A....
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This note was uploaded on 03/19/2014 for the course APMA 2130 taught by Professor Bernardfulgham during the Fall '09 term at UVA.

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