To be used for linear algebra, and closely related disciplines such as tensor algebras and maybe clifford algebras.

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Matrix separability preservation under conjugation?

Someone know any paper about matrix separability preservation under conjugation? A well know result is that Clifford group preserve the Pauli group under conjugation or, in other words: $C(P_{1} ...
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2answers
397 views

When and how do you represent a two body state as a tensor product?

I have read that in quantum mechanics, compound systems are constructed as tensor products. But on page 177 of Griffith, for example, a two body wavefunction is introduced as Psi ...
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202 views

Jacobi's matric formulation for tensors

Hi I am trying to derive the E field equation and am stuck using the Jacobi formula, is this correct: $$\delta \det g_{\mu \nu} = Tr(ADJ(g_{\mu\nu}\delta ...
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86 views

Why does the pure shear term / strain deviator tensor have non-zero entries on the main diagonal?

In a textbook of mine an operation is performed, of which I think the goal is to get zeros on the main diagonal of a matrix (the matrix represents strain). But im not sure that is the goal and Im also ...
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52 views

Eigenvector Grover Operator

I have a question about the eigenvectors for the evolution operator of Grover's algorithm. Let $U=R_DR_f$, where $$\begin{align*} R_D &= 2|D\rangle\langle D| -I_N , \\ R_f &= ...
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79 views

Writing a tensor with respect to a particular basis

When defining tensors as multilinear maps, I am having trouble understanding why a tensor, let's say of type (2,1), can be written in the following way: $$T = T^{\mu\nu}_{\rho} e_\mu \otimes e_\nu ...
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58 views

Time evolution in a static magnetic field of a 2-level system that is actually a 3 level system

What I want to do is describe the time evolution of only two states of a spin 1 particle on the bloch sphere. However, I'm running into trouble because I don't know how to construct the hamiltonian ...
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191 views

Lorentz boost matrix in terms of four-velocity

As I understand it, the value of a 4-vector $x$ in another reference frame ($x'$) with the same orientation can be derived using the Lorentz boost matrix $\bf{\lambda}$ by $x'=\lambda x$. More ...
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78 views

Eigenvalue $a_n$

Q1: In Zetilli's book page 166 (ch. "Postulates of QM", eq. 3.1) i encountered an expression $\hat{A}|\psi\rangle = a_n|\psi_n\rangle$. I know this is an eigenvalue equation, but i have seen another ...
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1answer
101 views

Confused on Calculating Resistance Distance Matrix

I am trying to create a computer program to compute the equivalent resistance over any points on any rectangular set of resistors (all with a resistance of 1 ohm). It seems that the resistance ...
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1answer
141 views

Cyclic rotation of a Matrix

What is meant by a cyclic rotation of a matrix, specifically in proving that j*k-k*j=i*l where j,k,l are cyclic rotations of the Pauli spin matrices sigma x, sigma y, and sigma z
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75 views

Trouble with proof about operators in QM

I would like to complete the following exercise: Prove that if the operators $P_i$ satisfy $P_i^{\dagger}$ = $P_i$ and $P_i^2$ = $P_i$, then $P_iP_j=0$ for all $i\neq j$. From $P_i^2 = P_i$ I ...
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51 views

Meaning of Eigenvalues/Eigenvectors of a linear system of equations

I have a 41x41 system of linear equations (inhomogen) which I derived with Eureqa by describing the timecourse of fMRI haemodynamic data from a brain area as a function of the timecourses of 40 other ...
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135 views

A simple question on the projected wave function?

For example, consider a spin-1/2 AFM Heisenberg Hamiltonian $H=\sum_{<ij>}\mathbf{S}_i\cdot\mathbf{S}_j$, and we perform a ...
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2answers
176 views

Will a one year undergraduate course of Linear Algebra be enough for QM? [duplicate]

Possible Duplicate: Linear Algebra for Quantum Physics Can you get all/most of the knowledge you need of Linear Algebra for QM in a one year course? I know for certain my course also ...
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1answer
118 views

Hamiltonian in 2-dimensions? [closed]

I am trying to construct a Hamiltonian for a system in 2 dimensions using Matlab. I am not sure how this Hamiltonian will look like in matrix form. If somebody can help me visualize this matrix that ...
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3answers
88 views

Eigenvectors of Pauli $\sigma_x$ matrix

I solve for eigenvectors of Pauli X matrix. I get {1,-1} and {1, 1}. In exercises I solve, there is an answer $\frac{1}{\sqrt{2}} $ * {1,1} and $\frac{1}{\sqrt{2}} $ * {1,-1}. Where does that ...
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3answers
973 views

Should linear algebra and vector calculus from traditional courses be replaced with `geometric algebra`? [closed]

geometric algebra gives geometric meaning to linear algebra and much more. it can provide a coordinate free geometric interpretation of spaces. those who learn of ...