2130_Chapter7_Notes

# amn some examples of matrices are given below 12 34

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Unformatted text preview: . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Exa (slide 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1 Matrix For both theory and computation, we review matrix theory in this section and the next. A matrix A is an m ¢ n rectangular array of elements (m rows and n columns) denoted by a11 a21 . . . Öaij × A a12 a22 . . . am1 am2 ¤¤¤ ¤¤¤ .. . ¤¤¤ a1n a2n . . . . amn Some examples of matrices are given below: 12 , 34 123 , 456 14 25. 36 2 / 17 Transpose The transpose of A Öaij × is AT Öaji×. Note that the rows become columns, and the columns become rows: a11 a12 a21 a22 A . . . ¤¤¤ ¤¤¤ a1n a2n a11 a21 a12 a22 . .. . . .. . . am1 am2 ¤¤¤ A . . . T am1 am2 . .. . . .. . . a1n a2n amn ¤¤¤ ¤¤¤ ¤¤¤ . amn Examples: 12 34 T 13 , 24 123 456 T 14 25. 36 3 / 17 2 Conjugate The conjugate of A × Öaij × is A aij , where x iy ¤¤¤ ¤¤¤ a11 a12 a21 a22 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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