## 1202 Reputation

17 years, 101 days

## What Is LaTeX ?...

I have no idea what LaTeX, is other than a helpful tool for publishing. However, I'd like to start using it for several reasons, but don't know where to begin. Can anyone suggest a very first starting point for someone in my position ? v/r, Thanks,

## Diagonalization Of Matrices...

A quick question to help with some Classical Mechanics homework. If the determinant of a matrix is zero does that mean that it cannot be diagonalized ? Please feel free to elaborate. I truly appreciate everyone's help on this site. In case your interested the text is "Classical Mechanics" 3rd ed. by Goldstein, Poole, and Safko. Chapter 4, specifically problem 4.8. Thanks, v/r,

## Group Theory Woes...

Show that an n x n unitary matrix has n^2 - 1 independent parameters. {Hint: Each element may be complex, doubling the number of possible parameters. Some of the constraint equations are likewise complex and count as two coordinates.} Next Question: The special linear group SL(2) consists of all 2 x 2 matrices (with complex elements) having a determinant of +1. Show that such matrices form a group. {Note: The SL(2) group can be related to the full Lorentz group in Section 4.4, much as the SU(2) group is related to SO(3). Taken from "Mathematical Methods For Physicists", Arfken and Weber.

## Normal Matrices...

Again we have the unitary and Hermitian matrices U and H related by, U = exp(i*a*H) (a) If the trace of H = 0, show that the determinant of U = +1. (b) If the determinant of U = +1, show that the trace of H = 0. Given Hint: H may be diagonalized by a similarity transformation. Then interpreting the exponential by a Maclaurin expansion, U is also diagonal. The corresponding eigenvalues are given by u[j] = exp(i*a*h[j] v/r, Guidance welcomed and appreciated

## Hermitian / Unitary Matrices...

Two matrices U and H are related by U = exp(i*a*H), where I assume a is a real constant, and i denotes the square root of -1. (a): If H is Hermitian, show that U is unitary. (b): If U is unitary, show that H is Hermitian. (H is independent of a.) Any advice or hints greatly appreciated, v/r, This is from the title "Mathematical Methods for Physicists" by Arfken and Weber. 6th ed. (section 3.4)
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