Tagged Questions

7
votes
1answer
256 views

Do these two sets of matrices form groups?

Stimulated by some Physics backgrounds, consider the following two sets of matrices. Notations and definitions:Let $A,B$ be two complex $n\times n$ matrices, then $\left [ A,B \right ...
2
votes
0answers
63 views

Solving Generalized Eigenvalue Problem perturbatively

Let me formulate the problem to convey my notation. I have a matrix $A$ which is hermitian - and is diagonalisable by a transformation $$ U_A A\,\,U_A^{-1} = A_{diag}$$ Now the matrix is changed, ...
1
vote
1answer
40 views

The representation of the resolvent of a quadratic form

I know some aspects are related each other concerning resolvent ,such a system of linear equation with a parameter, Fredholm theory and Green function method in nonlinear equation when I am reading ...
9
votes
3answers
525 views

What's the Clifford algebra?

I'm reading a book on Clifford algebra for physicists. I don't quite understand it conceptually even if I can do most algebraic manipulations. Can some-one teach me what the Clifford algebra really ...
0
votes
1answer
63 views

Find the parametric equation of the path of an object going at a speed x , with an orientation vector at time t and point p

$$ x = 1/2, v[2,−2], t = 3, P(1, 2)$$ x = speed, v = orientation, t = time, p is a point. I tried this : $$((2, -2) - (1,2)) \sqrt{1^2 + 4^2} $$ I got my <1,4> from $(2-1, 2-(-2))$ , which is my ...
0
votes
1answer
38 views

What is $\left(\delta_{ab}\right)^{-1}$?

I have an expression that involves the Wigner 3j coefficient: $$\left(\matrix{a&b&0\\0&0&0}\right)^{-1}$$ This simplifies to: ...
2
votes
1answer
105 views

Invariant polynomials

Let $A\in Mat_{2}(2\times2;\mathbb{R})$and consider the action of the 1-parameter group $e^{tA}$ on $\mathbb{R}^{2}$. Describe all 1-parameter groups etA which have a nonconstant invariant polynomial. ...