Lecture 7
... Both matrices on the LHS have rank one but their sum, the matrix on the RHS has rank two. Thus the set of matrices of rank at most one is not closed under addition. Similar examples pertain for any m and n > 1. Note however that the zero matrix has rank zero and a scalar multiple of a rank one matri ...
... Both matrices on the LHS have rank one but their sum, the matrix on the RHS has rank two. Thus the set of matrices of rank at most one is not closed under addition. Similar examples pertain for any m and n > 1. Note however that the zero matrix has rank zero and a scalar multiple of a rank one matri ...
Question 1 ......... Answer
... a2 x2 + . . . + an xn = 0, where at least one of the coefficients ai is nonzero. (a) [3 points] How many of the variables xi are free? What is the dimension of a hyperplane in Rn ? (b) [4 points] Explain what a hyperplane in R2 looks like, and give a basis for the hyperplane in R2 given by the equat ...
... a2 x2 + . . . + an xn = 0, where at least one of the coefficients ai is nonzero. (a) [3 points] How many of the variables xi are free? What is the dimension of a hyperplane in Rn ? (b) [4 points] Explain what a hyperplane in R2 looks like, and give a basis for the hyperplane in R2 given by the equat ...
The two-dimensional hydrogen atom revisited
... integral equation. Considering negative-energy 共bound-state兲 solutions, he projected the threedimensional momentum space onto the surface of a four-dimensional hypersphere. After a suitable transformation of the wavefunction, the resulting integral equation was seen to be invariant under rotations i ...
... integral equation. Considering negative-energy 共bound-state兲 solutions, he projected the threedimensional momentum space onto the surface of a four-dimensional hypersphere. After a suitable transformation of the wavefunction, the resulting integral equation was seen to be invariant under rotations i ...
