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A rank-one matrix is the product of two vectors. Ask Question Asked 8 years, 11 months ago. Modified 1 ...
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I doubt there is an analytic expression for all but the smallest matrix dimensions. However, there is an inexpensive way to compute the eigenvalues of rank-one update. The following comes from Demmel's Applied Numerical Linear Algebra subsection 5.3.3.
What is the rank if A is one to one? what about not one to one? I understand what rank is but i dont understand how you could find the rank just from knowing if a matrix is onto/one to one. And i dont get how it changes if its not onto/one to one
Quasiconvexity implies rank-one convexity. This was also known to Morrey and is not hard to check. Sverak showed in '92 that there exist functions which are rank-one convex but not quasiconvex. In particular, this means rank-one convexity does not imply lower semicontinuity. There is a huge literature on this topic; here are some themes covered:
Inverting identity plus a rank one matrix. Ask Question Asked 3 years, 4 months ago.
rank one update. Ask Question Asked 12 years, 6 months ago. Modified 12 years, 2 months ago. Viewed 4k ...
If you sum a certain number of rank-$1$ matrices: $$X = u_1 u_1^T + u_2 u_2^T + \\cdots + u_N u_N^T$$ Is the result guaranteed to be rank-$N$ assuming the individual ...
Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix 5 When is the matrix $\text{diag}(\mathbf{x}) + \mathbf{1}$ invertible?
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