homework02 - Homework 2 Stat 541 Linear Algebra Due Fri 12...

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Homework 2, Stat 541: Linear Algebra Due Fri, Sept 25, 2009, 12 Noon Your Name: (replace this with your name) September 22, 2009 Instructions: Edit this LaTex file by inserting your solutions after each problem statement. Generate a PDF file from it and e-mail the PDF to the usual class gmail address. You should not just answer the questions but also give evidence or even proof. You can discuss the homework with each other in general terms, but not with previous years’ students of Stat 541. Also, you must write your own solutions and not copy from anyone. 1. Interpretations of matrix multiplication: Assume X is of size n × p and B of size p × q . (a) If X = ( x 1 , x 2 , ..., x p ), B = ( b 1 , b 2 , ..., b p ) T , express XB = X j =1 ,...,p x j b T j A: (b) If X = ( x 1 , x 2 , ..., x n ) T , B = ( b 1 , b 2 , ..., b q ), express ( XB ) i,k = x T i b k A: 2. Write the Euclidean inner product as h x , y i = x T y and the Euclidean squared norm as k x k 2 = x T x . What is the interpretation of y 7→ h y , x i k x k 2 x ?
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