6 - MATHEMATICS 54 Professor Constantin Teleman 9/15/09...

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MATHEMATICS 54 Professor Constantin Teleman 9/15/09 Lecture 6 ASUC Lecture Notes Online is the only authorized note-taking service at UC Berkeley. Do not share, copy or illegally distribute (electronically or otherwise) these notes. Our student-run program depends on your individual subscription for its continued existence. These notes are copyrighted by the University of California and are for your personal use only. D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. ANNOUNCEMENTS Today we will talk about Matrix Algebra and Inverse Matrixes. Here is the outline: Review of matrix multiplication Transpose and properties Infectivity and subjectivity of linear transformation Invertible transformations and inverse matrices/ (LV factorization) LECTURE A m x n matrix linear map R n R m B n x p matrix linear map R p R n AB m x p matrix def Composed map R p B R n A R m Recall fg(x)=f(g(x)) Formulae for AB ( AB ) ij =(i th row of A)(j th row of B) = a i 1 .. a in [] b 1 j . . b nj = a i 1 b 1 j + a i 2 b 2 j ... a in b nj *The j th column of AB=A(j th column of B) *The i th row of AB= (i th row of A)B This last operation is a “left vector matrix product.” A r x n-component vector m-component vector r y T B : n-component row vector p-component row vector.
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6 - MATHEMATICS 54 Professor Constantin Teleman 9/15/09...

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