Notes-Chapter 4-Part 3

Notes-Chapter 4-Part 3 - LINEAR MODELS AND MATRIX ALGEBRA -...

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LINEAR MODELS AND MATRIX ALGEBRA - Part 3 Chapter 4 Alpha Chiang, Fundamental Methods of Mathematical Economics 3 rd edition
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Identity Matrix 2 3 1 0 0 1 0 0 1 0 0 1 0 0 1 I I = = Characteristics: It is like the number 1: a(1) = (1)a=a IA = AI = A
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Identity Matrix Special Nature of I Matrices : it is possible to insert or delete an I w/o affecting the matrix product. 2 ( ) Interesting case: if: ( ) ( ) mxn nxn nxp n n n n k n n A I B AI B AB A I AI I I I I = = = = = =
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Inverses and their Properties: For a given matrix A, The transpose is always derivable. Its inverse matrix (another type of derived matrix) may or may not exist. The inverse of matrix A is denoted by A -1 is defined only if A is a square matrix.
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1 1 1 1 1 1 1 1 1 1 1 ( ) ( ) ( ') ( )' AA A A I A A AB B A A A AA A A I - - - - - - - - - - - = = = = = = = Whether A is pre-multiplied or postmultiplied by A -1 , the product will be the same identity
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Notes-Chapter 4-Part 3 - LINEAR MODELS AND MATRIX ALGEBRA -...

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