(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am having trouble building a matrix in my post so I have attached the question (2.27) and my work thus far. I need to develop a matrixHwhich when multiplied by a vectorvproduces a new matrixUwith a constant 1/2 applied to certain terms of the matrix. Please see the attached matrix question for the final matrix which is desired. In the questionvis composed of n elements, where n=8. From this I have been able to deduce that my final matrix will be a 4 x 1, my matrix for representing the vectorvwill be an 8 x 1 matrix, which forces my input matrixHto be a 4 x 8 matrix, due to the rules of matrix multiplication.

2. Relevant equations

3. The attempt at a solution

I realized that my matrix H must have two entries of 1/2 in each row. As far as the original question, my method proves correct, but when I look at the second part of the question, part (b), it alludes to the fact that my matrixHmust be orthogonal, which in its current form it is not. I have attempted to place [tex]\frac{\sqrt{2}}{2}[/tex] in clever locations along the rows which gives me orthogonality, but it does not fit the final condition of each row in matrixUbeing composed of only two elements ofvand 1/2. Any help is greatly appreciated and sorry for the sloppy hand written solution. As an aside, can anyone let me know how to construct a matrix in this forum? Thanks in advance. BTW this problem is from the text "Discrete Wavelet Transformations: An Elementary Approach with Applications." by Patrick Van Fleet.

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# Homework Help: Construction of a matrix

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