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Category Archives: Uncategorized
Variance and the sum of squared pairwise differences
The variance of a set of values is usually expressed in terms of squared differences between those values and the mean of those values. However the sum of squared differences between the values and the mean can also be expressed … Continue reading
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All lengthpreserving matrices are unitary
I recently read the (excellent) online resource Quantum Computing for the Very Curious by Andy Matuschak and Michael Nielsen. Upon reading the proof that all lengthpreserving matrices are unitary and trying it out myself, I came to believe that there … Continue reading
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Linear Algebra and Its Applications, Exercise 3.4.22
Exercise 3.4.22. Given an arbitrary function find the coefficient that minimizes the quantity (Use the method of setting the derivative to zero.) How does this value of compare with the Fourier coefficient ? What is if ? Answer: We are … Continue reading
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Linear Alegbra and Its Applications, Exercise 1.6.17
Exercise 1.6.17. (a) Suppose that the n by n matrix A can be factored as LDU, where L and U have ones on the diagonal. Factor the transpose of A. (b) If we have what triangular systems will provide a … Continue reading
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Linear Algebra and Its Applications, Exercise 1.6.14
Exercise 1.6.14. For any m x n matrix A, prove that and are symmetric matrices. Provide an example where these matrices are not equal. Answer: Per Equation 1M(i) on page 47 we have Substituting for B we have Since is … Continue reading
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