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Apr 4, 2010 at 18:20 comment added Qiaochu Yuan Covariance matrices are essentially inner products, aren't they? That's just thinking of matrices as tensors of type (0, 2) instead of as tensors of type (1, 1). I think the theory of linear algebra is really good at clarifying the distinction between this type of matrix and the "usual" type of matrix; for example it gets to the heart of when similarity is relevant vs. when conjugation is relevant. So I don't think this is a good example.
Apr 2, 2010 at 2:24 history answered user1855 CC BY-SA 2.5