Lecture Notes 15

Lecture Notes 15 - Lecture15 1 October 24, 2007 Outline: 1)...

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Unformatted text preview: Lecture15 1 October 24, 2007 Outline: 1) Introducing the Determinant of a square matrix det(A) 2) Basic Properties: the big 3 3) More properties 4) Calculating |A| The Big Formula Calculation by Cofactors: Examples 5) Applications Cramer's Rule Volume and coordinate transformations Computing Eigenvalues Lecture 15: Everything you wanted to know about the Determinant |A| Formal Definition: The determinant of a square matrix A is the unique alternating , multilinear function that maps a matrix to a scalar such that det(I)=1. (this is not terribly informative though...) The Determinant of a square matrix A Notation: |A| or det(A) The determinant of a square matrix A is a function that maps the components of an nxn matrix to a number . 1) if A is singular, det(A)=0 2) the determinant of a 2x2 matrix Formal Definition: The determinant of a square matrix A is the unique alternating , multilinear function that maps a matrix to a scalar such that det(I)=1....
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Lecture Notes 15 - Lecture15 1 October 24, 2007 Outline: 1)...

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