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 Aug 23 revised Are these two Abel's criteria for uniform convergence different? added 32 characters in body Aug 23 asked Are these two Abel's criteria for uniform convergence different? Aug 23 accepted How is the joint distribution of random variables defined and determined? Aug 23 revised How is the joint distribution of random variables defined and determined? edited title Aug 22 revised How is the joint distribution of random variables defined and determined? added 68 characters in body Aug 22 asked How is the joint distribution of random variables defined and determined? Aug 22 comment Similarity between special matrices and special complex numbers Thanks! I feel the set of all n x n complex normal matrices instead of the set of all n x n complex matrices is analogous to the set of complex numbers. Is it right or wrong? Aug 21 comment What is the difference between matrix theory and linear algebra? Nice answer! Questions: (1) Are matrices always associated with vector spaces? Can they connect to the outside of vector spaces? (2) Is linear algebra the theory of vector spaces, or theory of both vector spaces and of matrices? Aug 21 revised Similarity between special matrices and special complex numbers added 9 characters in body Aug 21 asked Similarity between special matrices and special complex numbers Aug 21 accepted Conditions for a real matrix to have real eigenvalues Aug 21 comment What do Algebra and Calculus mean? @André: Nice! I was wondering if analysis and calculus mean the same thing, i.e. "a set of algorithms for solving a certain class of problems"? Aug 20 comment Conditions for a real matrix to have real eigenvalues @Theo: Why is this linear algebra? Are matrices always associated with vector spaces? Can they connect to the outside of vector spaces? PS: I identify linear algebra with the theory of vector spaces. Aug 20 revised Conditions for a real matrix to have real eigenvalues added 206 characters in body Aug 20 asked Conditions for a real matrix to have real eigenvalues Aug 20 comment Interpretation of matrices in vector spaces @anon, Dylan: Thanks for clarifying a lot. Aug 20 comment Interpretation of matrices in vector spaces Thanks! As to 1, I think the Gram matrix of a bilinear form and the matrix of a linear transform $V\rightarrow V^*$ induced by the bilinear from are different, so the usage of a matrix as a Gram matrix of a bilinear from and the usage of a matrix as that of a linear mapping are different. As to 3, I meant to ask what kind of special linear mapping a positive definite matrix directly represent, instead of indirectly by viewing the matrix as Gram matrix of a bilinear form and then considering the linear mapping induced by the form. Anon's comment on this might be in the right direction. Aug 19 revised Understanding positive definite kernel added 2 characters in body Aug 19 revised Understanding positive definite kernel added 32 characters in body Aug 19 comment Interpretation of matrices in vector spaces I want to ask if there are other usual ways to interpret a matrix in vector space theory.