I need to solve the lyapunov equation i.e. $A^TP + PA = -Q$. With $A = \begin{bmatrix} -2 & 1 \\ -1 & 0 \end{bmatrix}$ and $Q = \begin{bmatrix}1 &...

The answer is 2. But I want to learn how to simplify this expression without the use of calculator.

First of all, am I being crazy in thinking that if $\lambda$ is an eigenvalue of $AB$, where $A$ and $B$ are both $N \times N$ matrices (not necessarily i...

This is a lot simpler of a problem than others posted here, but I was bored in class and decided to work out why a horizontal asymptote exists. Bear in mi...

Question is from Spivak's Calculus 15-18. It asks to find the function $\arcsin(\cos x)$. Answer below: I have problem with the highlighted part. If ...

What is the greatest number of regions a plane can be divided into using $n$ straight lines? What about $n$ circles? Can you generalize this into 3-dimens...

Sorry if this is a bit simple compared to everything here, but I can't really seem to find an answer. If I have $$f(x) = \frac{(x-2)(x-4)}{x(x-1)}$$ ...

I've just started reading through Calculus Made Easy by Silvanus Thompson and am trying to solidify the concept of differentials in my mind before pr...

is there anyway to solve complicated roots without Calc e.g $S=108^{1/5}$ i always get stuck on these type of calculations. Calculator restricted here in ...

Is there a database somewhere of simple FOL statements, with their proofs written out in a Hilbert-style deduction system, or perhaps a tool to take such ...