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# Questions tagged [linear-algebra]

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

96 questions with no upvoted or accepted answers
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### Linear response theory for Gross Pitaevskii equation

I am trying to linearize the following GP eq: \begin{equation} i\partial_{t}\psi(r,t)=\left[-\frac{\nabla^{2}}{2m}+g\left|\psi(r,t)\right|^{2}+V_{d}(r)\right]\psi(r,t) \end{equation} The ansatz for ...
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### commutation relations for operators in projected subspaces

I am looking for a consistent re-definition of commutators for certain operators when I work in a projected subspace. Basically, I have a spin defined in terms of 4 Majorana operators $b_{x}$, $b_{y}$,...
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### Dropping vertices of an overdetermined statics system graph

In statics, the problem of determining the tensions of K cables that connect a structure made of N points and keep all points in static equilibrium implies $ND$ systems of equations, where $D$ is the ...
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### How coordinate system shifting is related to similarity transformations?

I know that coordinate system shifting can be represented using matrices. But how exactly are similarity transformations related to coordinate shifts ?
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### Finding an equivalent shape for a given mass and 3 mass moments of inertia

So I apologize if this is just impossible, but I was wondering if there was a way to find say, the dimensions of a box of a given density that would have the same mass and moments of inertia of ...
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### Hermitian phase operator and quantum harmonic oscillator

I need to apply a hermitian phase operator $\dfrac{1}{\sqrt{1+\hat{a}^\dagger\hat{a}}}\hat{a}$ to the nth harmonic oscillator state, but I have no idea how to interpret the square root of a ...
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### How to find the hermitian adjoint and inverse of an operator?

Suppose I have a translation operator defined as: $$\hat{T_a}\Psi(x)=\Psi(x+a) \, .$$ Now, how do I find the hermitian adjoint operator as well as its inverse?
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### Taking out % contribution of a zero order state from an eigenvector - dipole calculation

I am doing an analysis of a theoretical spectroscopy calculation. I take an eigenvector (nx1) and dot it with many zero-order dipole vectors (nx3) to get the dipole contribution to my new eigenstate. ...
In The Physics of Waves by Georgi, in Chapter 4, we show that, in a coupled system of masses connected by springs, a transformation that preserves some symmetry $S$ commutes with $K^{-1}M$. From my ...