HW - 2. In class we discussed the linear vector space of...

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Physics 591 - Homework Set # 1 Due: Monday, August 30 5 pm 1. Consider the set of real valued, two by two matrices. a) Show that this set is a linear vector space with the vector addition operator being matrix addition and give the dimension of the space. b) Is the following set a basis for this vector space? c) Can you deFne an inner product for this space with the operation of matrix multiplication? Why or why not? d) Show that you can you deFne an inner product by e) Use this inner product to construct an orthonormal basis.
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Unformatted text preview: 2. In class we discussed the linear vector space of functions of the form with p(x) a polynomial in x up to degree n-1, and we deFned an inner product Starting from the basis we used the Gram-Schmidt method to construct an orthonormal basis for the Frst 3 basis vectors. Extend this to the Frst Fve and check using a Table in any QM book that you have reproduced the Frst Fve Hermite polynomials....
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