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Mathematics : Recent Questions and Answers (Page 86)

Find answers to your questions about Mathematics or help others by answering their Mathematics questions.

Determine the lie algebra of the subgroup of SO(4)

Let $Gsubset SO(4)$be the subgroup given below: $$G=left{begin{pmatrix}a & -b & -c &-d\b & a & -d & c\c & d & a &...

Asked on 11/14/2021 by Shreedhar Bhat

3 answer

How to use general recursion to generate a set of words?

I am just getting to recursion in one of my classes, and I'm a bit confused on how to go about generating a set of words and the notation. Given...

Asked on 11/14/2021 by Pwelb

2 answer

Calculate Hessian of a "weird" function

let be $L $ an invertible matrix, $b in mathbb{R}^{n}$ and $mu in mathbb{R}$ and $J: mathbb{R}^{n} rightarrow mathbb{R}$ defined as $J(x)=|L x|_{2}^{2}+mu...

Asked on 11/12/2021 by Ben Schneider

2 answer

Find volume under given contraints on the Cartesian plane.

The constrains are given as $$x^2+y^2+z^2 leqslant 64,,x^2+y^2leqslant 16,,x^2+y^2leqslant z^2,,zgeqslant 0,.$$ With the goal of finding the Volume.Personally, I have trouble interpreting the constrains in terms of integrals...

Asked on 11/12/2021 by Pavel Fedotov

2 answer

Equivalence of Classical Nullstellensatz to "Affine schemes have points"

The nLab page on the Nullstellensatz states:For $k$ an algebraically closed field and $I$ a proper ideal in the polynomial ring $k[X_1, dots, X_n]$, the...

Asked on 11/12/2021

1 answer

A donut shop sells 12 types of donuts. A manager wants to buy six donuts, one for himself and 5 for his employees.

I'm reading Advanced Combinatorics by Mitchell T. Keller and William T. Trotter and it's missing an answer book (or, at least, I couldn't find one.) I've been...

Asked on 11/12/2021 by Daniel Sidorkin

1 answer

A compact normal operator is diagonalisable.

Consider the following proof in Murphy's book: "$C^*$-algebras and operator theory": I try to understand why $u(K^perp) subseteq K^perp$. Equivalently, one...

Asked on 11/12/2021 by user745578

1 answer

If complex matrices $A$, $B$, $AB-BA$ are nilpotent, show that $A+B$ is nilpotent.

Let $A$ and $B$ be square complex matrices, and $C=[A,B]=AB-BA$. Suppose that $A$, $B$, and $C$ are nilpotent. When $A$ and...

Asked on 11/12/2021 by Rex Wang

0 answer

Integral with an index

I have an economic problem where it is claimed that the production of final goods is given by the following integral $$Y=int_{i=0}^{i=1}x_idi$$ where $x_i$ is the...

Asked on 11/12/2021

1 answer

How do I find the probability distribution of a dependent variable given the probability distributions of its independent variables?

I have two probability distribution functions, $F$ and $G$, describing quantities $x$ and $y$ respectively. Both $x$ and $y$ are required to find quantity...

Asked on 11/12/2021 by TempUserPerson

0 answer

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