Recent content by Mathsadness
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Undergrad Definiteness of a nonsymmetric matrix
Can you please elaborate a bit? Wouldn't the process I mentioned above apply i.e making the matrix symmetric first and then use the usual procedure?- Mathsadness
- Post #3
- Forum: Linear and Abstract Algebra
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Undergrad Definiteness of a nonsymmetric matrix
There is no specific example but my attempt at one would be to make the non-symmetric matrix symmetric. Then we would be able the usual formulas as designed for symmetric matrices. Is this how it works? Alternatively, do I just calculate the Eigen values without making it symmetric? I don't...- Mathsadness
- Thread
- Matrix
- Replies: 4
- Forum: Linear and Abstract Algebra
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Undergrad Why is [0,1] compact in the case of a collection of open neighborhoods?
Can you explain the part why 1/n does not converge to a point in (0,1)? Is it because we define limit as |1/n-0|<e, which boils down to 1/n<e which can be made arbitrarily small by archimedean property? Essentially saying that 1/n=0. As 0 is not in (0,1) it converges in [0,1]?- Mathsadness
- Post #5
- Forum: Topology and Analysis
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Undergrad Why is [0,1] compact in the case of a collection of open neighborhoods?
For (0,1), the collection of neighborhoods N_e of q from (0,1) is an open cover. However, there exists e>0 such that it will not have a finite sub cover. Let us take e=0.5*min{|p-q|}, where p=/=q and both are from (0,1). I am not sure if the construction of e here is right, please correct me if...- Mathsadness
- Thread
- Compact
- Replies: 9
- Forum: Topology and Analysis