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 Aug 22 comment Determinant of a special skew-symmetric matrix @J.M., wrote up the answer. Aug 22 answered Determinant of a special skew-symmetric matrix Aug 22 comment Determinant of a special skew-symmetric matrix @J.M., the key is that for $n=2$, $\mathbf{E}^{-1} = \mathbf{E}^T$, so $\mathbf{F}^T \mathbf{E}^{-1} \mathbf{F} = \mathbf{F} \mathbf{E}^T \mathbf{F}$. From there, it is straightforward to show that it must be zero. Overall, it may make the induction of the entire problem easier if $\mathbf{H}$ and $\mathbf{E}$ were swapped. Aug 21 comment Deriving the inverse of $\mathbf{I}$+Idempotent matrix I am interested in more detail, if you would. A reference would be sufficient. Aug 16 comment For this bilinear form: $q(v)=q(x_1,x_2,x_3)=x_1^2+x_2^2+9x_3^{2}+2x_1x_2-6x_1x_3-5x_2x_3$ find a base $B$ so that $[q]^B_B=D$ diagonalizable matrix Your matrix has a mistake in it, the $x_2 x_3$ term (2.5) should be negative. Aug 13 comment Given $A\in M_{6}$ and $f(x)=2x^9+x^8+5x^3+x+a$, for what values of $a$ is $f(A)$ invertible? @Didier, you are correct. It assumes that $A$ is not defective, as it is here. Aug 13 comment Given $A\in M_{6}$ and $f(x)=2x^9+x^8+5x^3+x+a$, for what values of $a$ is $f(A)$ invertible? @Nir, what is $f(A)$ when $A$ is diagonal? Also, let $A = S^{-1}DS$, where $D$ is diagonal, then what is $A^n$? You can use those results to show that $f(\lambda)$ is an eigenvalue of $f(A)$. Aug 9 comment Conserved Quantities in Dynamical Systems As a point of note, this site operates on accumulated reputations which is acquired via others voting on the questions and answers you have posted and possible having your answers accepted as the best/correct one. For this system to work, you should vote on the answers you find useful, and accept those answers which best answer your questions. To do otherwise, in the long term you will eventually find your questions being ignored. Aug 5 answered Conserved Quantities in Dynamical Systems Aug 5 revised Conserved Quantities in Dynamical Systems fixed typo; added LaTeX markup Aug 5 suggested approved edit on Conserved Quantities in Dynamical Systems Jun 12 comment Divergence as transpose of gradient? I've been looking at those formulas for years, and that is probably the most intuitive form I've seen. To be clear, since $g$ is a "scalar", then $\nabla^T g = (\nabla g)^T$, or have I misinterpreted it? Jun 12 comment Completing the squares for matrices As written, the first equation does not make sense. The first term is a scalar, but the other terms are vectors, presuming that $A$ and $B$ are matrices. Does the missing $C$ fix that? In truth, none of equations make sense for the same reason. Jun 9 comment Determine the matrix relative to a given basis +1, didn't think of that, but I should have. Jun 4 revised Maximizing a function by finding derivative added align so that equation would fit in bounding box Jun 4 suggested approved edit on Maximizing a function by finding derivative Jun 3 revised Limit of a Markov transition matrix moved comma; rearranged code for clarity Jun 3 suggested approved edit on Limit of a Markov transition matrix Jun 3 revised Inverting the sum of a Dense and Diagonal matrix added additional thoughts on second question Jun 3 comment Inverting the sum of a Dense and Diagonal matrix @Eric, I went through the same set of trials with my research, so batting zero is average! I'd recommend the books by G. W. Stewart (1, 2). Eventually, there will be 5 volumes, but the first two alone will improve how you think about matrix problems.