2022-02-10
Answered

Define adjoint of operators

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Answered 2022-02-14

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Vasquez

Answered 2022-03-13
Author has **460** answers

Adjoint operators mimic the behavior of the transpose matrix on real Euclidean space. Recall that the transpose satisfies

asked 2022-04-10

Suppose that R is a commutative ring and |R| = 30. If I is an ideal of R and |I| = 10, prove that I is a maximal ideal

asked 2022-06-23

The statement-title above is a result that should follow from the hint I got to solve it: "Show that the inversion map $i:G\to G\text{},\text{}g\u27fc{g}^{-1}$ is a Lie group homomorphism if $G$ is commutative, and then study the resulting Lie algebra homomorphism." The first part of this hint was easy, but I am not getting any further. I think the corresponding homomorphism should be the total derivative of i evaluated in the identity of $G$ , but I'm not getting anywhere with this idear yet.

I think the trivial Lie bracket should be $[X,Y]=0$ for two vector fields on $G$, which holds iff the corresponding flows of $X$ and $Y$ commute.

I think the trivial Lie bracket should be $[X,Y]=0$ for two vector fields on $G$, which holds iff the corresponding flows of $X$ and $Y$ commute.

asked 2021-09-23

Find the directional derivative of the function at the given point in the direction of the vector v. $f(x,y)=\frac{x}{{x}^{2}}+{y}^{2},(1,2),u=<3,5>$

asked 2022-01-31

Let $T:{R}^{3}\to {R}^{3}$ be the linear transformation such that

$T\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]=\left[\begin{array}{c}-2\\ 5\\ -2\end{array}\right],{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}T\left[\begin{array}{c}1\\ 1\\ 0\end{array}\right]=\left[\begin{array}{c}4\\ 1\\ 4\end{array}\right],{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}T\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]=\left[\begin{array}{c}1\\ -1\\ 1\end{array}\right]$

a) Find a matrix A such that$T\left(x\right)=Ax$ for every $x\in {R}^{3}$

b) Find a linearly independent set of vectors in$R}^{3$ that spans the range of T

a) Find a matrix A such that

b) Find a linearly independent set of vectors in

asked 2021-06-11

Table shows the number of wireless service subscribers in the United States and their average monthly bill in the years from 2000 through 2015

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One of the scatter plots suggests a linear model. Use the points at t = 0 and t = 15 to find a model in the form y = mx + b.

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Let A be an uncountable set, B a countable subset of A, and C the complement of B in A. Prove that there exists a one to one correspondence between A and C.

asked 2021-08-20

By using the transformation of function $y=\mathrm{cos}x$ , sketch the function of $y=-\mathrm{cos}(3x-\frac{\pi}{6})+4$