2130_Chapter7_Notes

E a is an n n matrix a11 a21 a a12 a22 a1n a2n an1

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Unformatted text preview: Example: A a1n a2n × A . .. . . .. . . am1 am2 ¤¤¤ x ¡ iy : amn a11 a12 a21 a22 . . . × A a1n a2n ¤¤¤ amn . .. . . .. . . am1 am2 1 2 3i 4 3 ¡ 4i ¤¤¤ ¤¤¤ . 1 2 ¡ 3i . 4 3 4i 4 / 17 Adjoint The adjoint of A Öaij × is A¦ × AT aji : a11 a12 a21 a22 A . . . A a1n a2n ¤¤¤ amn A¦ . .. . . .. . . am1 am2 Example: ¤¤¤ ¤¤¤ a11 a21 a12 a22 . . . A¦ am1 am2 ¤¤¤ amn . .. . . .. . . a1n a2n 1 2 3i 3 ¡ 4i 4 ¤¤¤ ¤¤¤ 1 3 4i . 2 ¡ 3i 4 5 / 17 3 Square Matrix A square matrix A has the same number of rows and columns; i.e., A is an n ¢ n matrix: a11 a21 . . . A ¤¤¤ ¤¤¤ a12 a22 . . . .. a1n a2n . . . . ¤¤¤ an1 an2 . ann Examples: A 12 , 34 B 123 456. 789 6 / 17 Vectors A column vector x is an n ¢ 1 matrix. For example, 1 2. 3 x A row vector y is an 1 ¢ n matrix. For example, y Note that y 1 2 3. xT , and that in general, if x is a column vector, then xT is a row vector. 7 / 17 4 Matrix Equality Two matrices A Öaij × and B Öbij × are equal only if aij bij for all i and all j. This means tha...
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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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