It doesn't help me, because I plan to show that the transformation is Hermitian by the following theorem:
"If T is a normal transformation whose Characteristic polynomial can be completely factored into linear factors over \mathbb{R}, then T is Hermitian".
And then it follows, of course, that...
Homework Statement
let T:V \to V be a linear transformation which satisfies T^2 = \frac{1}{2} (T + T^*) and is normal. Prove that T=T^*.
Homework Equations
The Attempt at a Solution
I think we should start like this:
Let \mathbf{A}=[T]_B be the matrix representation of T in the...
Homework Statement
Use an appropriate double integral and the substitution
y = br\sin \theta \text{\ \ \ } x = ar\cos \theta
to calculate the bounded area inside the curve:
{\left( \frac{x^2}{a^2} + \frac{y^2}{b^2} \right)}^2 = \frac{x^2}{a^2} - \frac{y^2}{b^2}
(you can...
What do you mean to solve the equation "for" something?
I suppose I could isolate the \frac{\partial \varphi}{\partial t} if I knew it's multiplier wasn't zero...
Edit:
I did that. It leads to nothing.
It's obvious that I miss something obvious but after a week on this problem and a dead-line...
Yep, I know that chain rule. We get:
2x + 2z \frac{ \partial z }{ \partial x } = \frac{ \partial \varphi } { \partial t } \left( a + c \cdot \frac{ \partial z }{ \partial x } \right)
and:
2y + 2z \frac{ \partial z }{ \partial y } = \frac{ \partial \varphi } { \partial t } \left( b +...
Homework Statement
Calculate the sum of the following series:
\sum_{i=2}^{\infty}(-1)^i \cdot \lg ^{(i)} n
Where (i) as a super-script signifies number of times lg was operated i.e. \lg ^{(3)} n = (\lg (\lg (\lg n))) , and n is a natural number.
Homework Equations
The Attempt...
Hello,
I see that a common method to calculating limits is a change of the variable. For example, to calculate:
\lim_{x \to \infty} \sin x \cdot \sin \frac {1}{x}
We say that
t=\frac{1}{x}
and then:
\lim_{x \to \infty} \sin x \cdot \sin \frac {1}{x} = \lim_{t \to 0^+} \sin...