Reputation
929
Top tag
Next privilege 1,000 Rep.
Create new tags
Badges
1 8 20
Newest
 Caucus
Impact
~36k people reached

Sep
25
comment Do real matrices always have real eigenvalues?
@commenter, no. The equation $A v = \lambda v$ has a non-trivial solution iff $\det(A - \lambda I) = 0$ which is identical to finding the roots of a polynomial in $\lambda$. We know the roots of a polynomial with real coefficients may have complex roots. If we try to restrict ourselves to only real roots, we're not guaranteed to find all of them.
Sep
25
awarded  Critic
Sep
25
comment Do real matrices always have real eigenvalues?
No, it doesn't. Finding the eigenvalues of a matrix is identical to finding the zeroes of a polynomial, and polynomials with real coefficients can have complex zeroes. Consider $(a - \lambda)(b - \lambda) - c d = 0$ which has complex roots if $(a+b)^2 < 4 (ab - cd)$.
Sep
24
revised Solving an equation with trig functions and two different angles
added LaTeX markup
Sep
24
suggested approved edit on Solving an equation with trig functions and two different angles
Sep
24
answered Pure maths vs applied
Sep
22
revised derivatives using chain rule
deleted 2 characters in body
Sep
22
answered derivatives using chain rule
Sep
22
comment Derivative using product rule and chain rule
As a second point, I'm not a fan of Newtonian notation to indicate a derivative, e.g. $f'(x)$, and I prefer Leibniz's, e.g. $df/dx$, because it is difficult to tell which variable to use when calculating a derivative like, $\cos(a^3 + x^3)'$. In first semester calculus, this is easier as it is likely to be $x$. But, Leibniz's notation leaves less room for ambiguity, and that can be a life saver when doing these. However, professors insist on using Newton's form, so you have to learn it, also. But, I'd change it to the other form when working these.
Sep
22
awarded  Citizen Patrol
Sep
22
comment Derivative using product rule and chain rule
This is just a relatively straightforward application of your previous question. I'd suggest looking at Jonas' answer again.
Sep
12
awarded  Analytical
Sep
8
revised Determinant and power series
added align environment: formula exheeded bounding box.
Sep
8
suggested approved edit on Determinant and power series
Aug
27
comment How to solve a system of dot products
You have a $t$ in the denominator of the $b$ term in your known solution. Is that supposed to be a $\tau$?
Aug
27
comment Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even
Great solution. My only question is what led you to it? Most likely it was the observation that $(2)$ is true, but I'm curious about the thought process.
Aug
22
revised Determinant of a special skew-symmetric matrix
clarified
Aug
22
revised Determinant of a special skew-symmetric matrix
added link; rearranged for clarity
Aug
22
revised Determinant of a special skew-symmetric matrix
fixed typo
Aug
22
revised Determinant of a special skew-symmetric matrix
deleted 1 characters in body