Consider a matrix pencil of quadratic form $F + \lambda B$ with $F, B$ are symmetric and positive definite.
For which $\lambda$ is $F + \lambda B \geq 0$?
Matrix pencil of quadratic form $F + \lambda B$
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matrices
quadratic-forms
1 Answers
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If "greater or equal to $0$" means positive semidefinite, this is true for $\lambda \ge -\epsilon$ for some $\epsilon > 0$.