Transcription of Linear algebra cheat-sheet - Laurent Lessard
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Linear algebra cheat-sheetLaurent LessardUniversity of Wisconsin MadisonLast updated: October 12, 2016 Matrix basicsA matrix is an array of Rm nmeans that:A= (mrows andncolumns)Two matrices can be multiplied if inner dimensions agree:C(m p)=A(m n)B(n p)wherecij=n k=1aikbkjTranspose: The transpose operatorATswaps rows andcolumns. IfA Rm nthenAT Rn mand (AT)ij=Aji. (AT)T=A. (AB)T= basics (cont d)Vector products. Ifx,y Rnare column vectors, Theinner productisxTy R( dot product) Theouter productisxyT Rn are just ordinary matrix multiplications!
Oct 12, 2016 · Linear algebra cheat-sheet Laurent Lessard University of Wisconsin{Madison Last updated: October 12, 2016. Matrix basics A matrix is an array of numbers. A 2Rm n means that: A = 2 6 4 a ... When the linear equations Ax = b are overdetermined and there is no solution, one approach is to nd an x that almost works by minimizing the 2-norm of the ...
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