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I am reading some lecture notes where it states that the difference of two metrics needs to be weakly positive definite. Since the metric is a symmetric bilinear form, I take it that this means that the difference of the quadratic forms associated with the two metrics needs to be positive definite, but I am not sure what it means for a quadratic form to be weakly rather than strictly positive definite. I did try to look it up but did not find an answer. Does it mean positive semi-definite?

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