Lecture Notes 4

# Lecture Notes 4 - Lecture 04 Lecture 04: Systems of Linear...

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Lecture 04 1 September 13, 2007 Outline: 1) Matrix-Matrix Operations (the rules of the game) Matrix Multiplication: AB Block Matrices Proof of Associative law A(Bc )=(AB)c Computational Costs Matrix Powers: A p 2) The Matrix Inverse: A -1 (square matrices) Fun Facts about A -1 The inverse of simple matrices (I,D,E,P) The inverse of General matrices: Gauss-Jordan Elimination Lecture 04: Systems of Linear Equations #3: General rules of Matrix-Matrix Operations Matrix Matrix Multiplication: C=AB General rules of Matrix-Matrix Operations Matrix Matrix Multiplication: C=AB Examples: General rules of Matrix-Matrix Operations Properties of Matrix-Matrix Multiplication: Block Matrices: Examples:

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Lecture 04 2 September 13, 2007 Proof of Associative property for Matrix Multiplication Theorem: Matrix Mult is associative. If A,B,C are matrices of appropriate shapes, then A(BC)=(AB)C Proof (sketch): Show A(Bc )=(AB)c Another important Digression: Operation costs Matrix-vector and Matrix-Matrix multiplication
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## This note was uploaded on 06/02/2010 for the course APMA APMA E3101 taught by Professor Spiegelman during the Fall '07 term at Columbia.

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Lecture Notes 4 - Lecture 04 Lecture 04: Systems of Linear...

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