2130_Chapter7_Notes

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This note was uploaded on 03/19/2014 for the course APMA 2130 taught by Professor Bernardfulgham during the Fall '09 term at UVA.

Ask a homework question - tutors are online