Recent content by LeifEricson

Can someone help me please? I work on it two days. Nothing works. Please. I spent hours.

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...

Oh no! You are right. The substitution I wrote is a mistake. I will edit my post to fix that.

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 Given: \varphi(t) – differentiable function. z=z(x,y) – differentiable function. And there is the following equation: x^2 + y^2 + z^2 = \varphi (ax+by+cz) where a,b,c are constants, Prove that: (cy - bz)\cdot \frac {\partial z}{\partial x} +...

You are right. The series isn't well defined so I cancel this question. I apologize.

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...