Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 114

A matrix cannot be expressed as a sum $B+C$ with $B^2=B$ and $C^3=0$

Let $$A=begin{bmatrix} 0 & 0 & 0 & 1 \1 & 0 & 0 & 0 \0 & 1& 0 & 0 \0 & 0 &...

Asked on 02/21/2021 by Mashed Potato

1 answer

Trigonometric system with two unknowns

Right now I had a question about a trigonometric system of equations and I got very good ideas. However after some modifications to the system I reached another one and...

Asked on 02/21/2021 by Melisa Karimi

0 answer

Noncompact (Lie) group has no faithful, finite dimensional, and unitary representations?

In class, a professor said:Noncompact (Lie) group has no faithful, finite dimensional, and unitary representations.Does this statement hold for noncompact group that is not a Lie group?Can we loosen one...

Asked on 02/21/2021 by annie marie heart

2 answer

How to denote a one to one mapping between $A = { B,C,D}$ and $B = { {X_1},{X_2},{X_3}}$?

How to denote there exist a one to one mapping with order between the set $A = { B,C,D}$ and the set $B = { {X_1},{X_2},{X_3}}$ ? Particularly,...

Asked on 02/21/2021 by Tuong Nguyen Minh

0 answer

Evaluate $int_{0}^infty frac{sin(x)}{sqrt{x^2+1}} dx$

The first substitution that came to my mind was$$begin{cases}x = tan(theta) \dx = sec^2theta dtheta \textrm{Bounds:} , , 0 to , pi/2end{cases}$$...

Asked on 02/20/2021 by Stanislas CASTELLANA

1 answer

Dimension of the intersection of $k > n$ hyperplanes

Suppose there is an $n$-dimensional affine subspace - let us call it $S$ of$mathbb{R}^d$, $d>n$. Suppose we have $k>n$ hyperplanes in $mathbb{R}^d$. We...

Asked on 02/20/2021 by Canine360

1 answer

Existence of a monotonic-decreasing function with monotonically increasing log derivative

For reasons that are completely absurd, I'm interested in whether such a function $f$ (as briefly described in the title) exists: $f$ is smooth on the interval ...

Asked on 02/20/2021 by Sam Blitz

0 answer

For a square matrix $A$, if $AB = 0$ for some nonzero $B$ then $CA = 0$ for a nonzero matrix $C$.

I've been asked to prove that the following statements are equivalent for any $n$x$n$ matrix $A$:(Note that A and B both are $n$x$n$)$AB...

Asked on 02/20/2021

3 answer

Regular differentials on a singular curve.

Let $X'$ be an irreducible singular algebraic curve over an algebraically closed field $k$, and let $X to X'$ be its normalization, and consider a (singular) point...

Asked on 02/20/2021 by red_trumpet

0 answer

For which $N$ is it possible to arrange all whole numbers from $1$ to $N$ in such a way that every adjacent pair sums up to a Fibonacci number?

Recently I came up with a problem regarding Fibonacci numbers:For which $N$ is it possible to arrange all whole numbers from $1$ to $N$ in such a...

Asked on 02/20/2021 by Rubenscube

1 answer

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