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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
Aug
3
comment Is this Batman equation for real?
One answer, five badges: Nice Answer, Mortarboard, Good Answer, Great Answer, Guru. Nice haul all told.
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