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Pancake_Senpai
  • Member for 7 years, 4 months
  • Last seen more than a month ago
22 votes
6 answers
5k views

What is wrong with this proof that symmetric matrices commute?

19 votes
5 answers
389 views

Intuition for why $f_{xy} = f_{yx}$

7 votes
2 answers
4k views

Intuition for the invariance of the determinant under change of basis

2 votes
2 answers
1k views

Does every (complex) $n\times n$ matrix have n linearly independent eigenvectors?

2 votes
2 answers
74 views

How to find the radius of convergence of $\sum^{\infty}_{n=1}\frac{n!}{n^n}z^n$?

1 vote
1 answer
88 views

How to prove that the product of two matrix sums is commutative.

1 vote
1 answer
60 views

Value of a definite integral changes when rearranging the integrand.

1 vote
1 answer
2k views

How to work out percentage change with inverse proportionality?

1 vote
1 answer
278 views

Particular integral for inhomogeneous term $\cos(ax)\sin(bx)$?

1 vote
1 answer
815 views

Why does the order of integration matter for the function $f(x,y)=y$?

1 vote
1 answer
189 views

How to prove that eigenvalues of a symmetric matrix with respect to a metric are real, and that there always exists an eigenbasis?

1 vote
0 answers
62 views

Why is an integral treated like a summation?

1 vote
2 answers
101 views

Does $\frac{z^2}{(z^2-1)^{\frac{1}{2}}}$ have a simple pole at $\infty$?

1 vote
1 answer
2k views

How to work out $\int^{2\pi}_0\frac{1}{3+2\cos\theta+\sin\theta}\,d\theta$ using contour integration?

1 vote
1 answer
353 views

Prove that $\int^\infty_0\cos(ax^2) dx = \sqrt{\frac{\pi}{8a}}$ using Cauchy's theorem $\oint_C f(z)dz=0$

0 votes
2 answers
81 views

How to integrate the differential equation $\frac{dx}{dt}=a(x-c)^2-bx^2$ given initial condition

0 votes
1 answer
45 views

What is $\nabla \times d\vec{r}$?

0 votes
1 answer
62 views

Does $\widehat{M}\ (\vec{a}\times\vec{b})=\widehat{M}\ \vec{a}\times\widehat{M}\ \vec{b}$?

0 votes
0 answers
56 views

If $U^{\lambda}T_{\lambda}^{\mu}=0$ and $U^{\lambda}$ is a vector, can we state that $T_{\lambda}^{\mu}$ is a tensor by the quotient rule?

0 votes
0 answers
284 views

Why does the Discrete Fourier Transform give frequencies higher than the Nyquist frequency?

0 votes
0 answers
22 views

What is the name for a portion of a spherical segment?

0 votes
1 answer
94 views

How to find the integrating factor for this ODE?

0 votes
1 answer
30 views

Struggling to prove that the elements of an inverse matrix satisfy a certain equation.

0 votes
3 answers
1k views

Does $\mathbf{a}\,.\mathbf{a} = \mathbf{a}\,.\mathbf{b}$ mean that $\mathbf{a}=\mathbf{b}$?

0 votes
2 answers
217 views

Integrating $\int\frac{\cosh(2y)\cos(2x)-1}{(\cosh(2y)-\cos(2x))^2}dy$

0 votes
2 answers
413 views

How to find the particular integral of an ODE with an inhomogeneous component formed from the sum of exponentials and powers of trig?

0 votes
2 answers
163 views

How to prove that a $3\times 3$ matrix has only $2$ eigenvectors?

0 votes
4 answers
82 views

How to solve $\frac{dy}{dx}\ln(x)+\frac{2y}{x}=1$?