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Results tagged with matrix-analysis
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user 70621
The study of the properties of real and complex matrices that are more close to analysis and operator theory. For instance: the properties of positive definite matrices, matrix inequalities, perturbation analysis, matrix functions, inequalities between eigenvectors and singular values, majorization.
3
votes
If $A>B>0$, can we always find a positive real number $\alpha$, $0<\alpha < 1$ such that $\a...
The @Alex Ravsky's answer is good, however, I still want to share my answer:
Proof: To prove $\alpha A\geq B$ where $0<\alpha<1$, we introduce an extra parameter $\lambda$, $0<\lambda<1$, $\alpha=1-\ …
- 161
2
votes
2
answers
269
views
If $A>B>0$, can we always find a positive real number $\alpha$, $0<\alpha < 1$ such that $\a...
Suppose we have positive-definite matrices $A$, $B$, if $A>B>0$, can we always find a positive real number $\alpha$, $0<\alpha < 1$ such that $ \alpha A \geq B $? If it has, then what is it?
- 161