# Questions tagged [linear-algebra]

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

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### Raising and Lowering Operators of a Hamiltonian

Lets say that I have a Hermitian Hamiltonian $H$ with a non-Hermitian raising operator operator $A$ which satisfies \begin{equation} [H,A] = \Omega A, \quad \Omega \in \ \mathbb{R}_{>0}. \end{...
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### Defining an inner product over matrices and over vectors

In quantum mechanics, in Dirac notation an inner product is denoted as $\langle A|B\rangle$ and one fundamental postulate is given as follows: $\langle A|B\rangle = \langle B|A\rangle ^*$ If I were to ...
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### Examples of antiunitary operator other than time reversal operator

It is well-known that time reversal operation is implemented as an anti-unitary operator. I wonder what are some other examples of anti-unitary operators that appear in the context of quantum ...
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### Visualization of $n$-dimensional Hilbert spaces

I am learning quantum physics, and came across $n$-dimensional Hilbert spaces, is there any way one can visualize a $n$-dimensional space and the n components of the vectors existing in that space? P....
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### Matrix representation of transformation defined on creation operators - Bogoliubov transform

In this paper by Alba Cervera-Lierta the following transformation is performed: $$a_k=u_kc_k+iv_kc^\dagger_{-k} \\ a^\dagger_k=u_kc^\dagger_k-iv_kc_{-k}$$ where $c_k$ and $a_k$ represent ...
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### Representing Quantum Gates in Tensor Product Space

I want to write the matrix form of a single or two qubit gate in the tensor product vector space of a many qubit system. Ill outline a simple example: Both qubits, $q_0$ and $q_1$ start in the ground ...
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### Verifying the Gaussian Transformation of $exp\left\{\frac{1}{2}\sum_{i,j} S_i J_{ij} S_j\right\}$ from “Advanced Mean Field Methods”

The book Advanced Mean Field Methods mentions the following equation as a result of a "simple gaussian transformation".  exp\left\{\frac{1}{2}\cdot\textbf{s}^T \cdot \textbf{J} \cdot\textbf{s}\...
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### Phase portrait with python using Jordan and eigenvalues

I want to make a phase portrait on python. I have 3 Ode's. I know the Jordan canonical form. And i know the eigenvalues. So i know when it is stable. Does anybody know how I can make a portrait using ...
Suppose I have a state expressed in its eigenbasis as follows. $\rho = \sum_i\lambda_i\vert i\rangle\langle i\vert$. It is now measured in some other basis $\{\vert x\rangle\}$ that is distinct from ...