# Tagged Questions

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

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### Are matrices and second rank tensors the same thing?

Tensors are mathematical objects that are needed in physics to define certain quantities. I have a couple of questions regarding them that need to be clarified: Are matrices and second rank tensors ...
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### Linear Algebra for Quantum Physics

A week ago I asked people on this site what mathematical background was needed for understanding Quantum Physics, and most of you mentioned Linear Algebra, so I decided to conduct a self-study of ...
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### Importance of Kronecker product in quantum computation

To get product state of two states $|\phi \rangle$ and $|\psi \rangle$, we use Kronecker product $|\phi \rangle \otimes |\psi \rangle$. Instead of Kronecker product $\otimes$, can we use Cartesian ...
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### Difficulties with bra-ket notation

I have started to study quantum mechanics. I know linear algebra,functional analysis, calculus, and so on, but at this moment I have a problem in Dirac bra-ket formalism. Namely, I have problem with "...
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### How to take partial trace?

$L$ is a linear operator acting on hilbert space $V$ of dimension $n$, $L: V \to V$. The trace of a linear operator is defined as sum of diagonal entries of any matrix representation in same input ...
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### Conceptual difficulty in understanding Continuous Vector Space

I have an extremely ridiculous doubt that has been bothering me, since I started learning quantum mechanics. If we consider the finite dimensional vector space for the spin$\frac{1}{2}$ particles, ...
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### “An operator is hermitian”. Implications?

Alastair Rae states that there are 4 postulates of Quantum Mechanics in his text on the subject matter. The first part of his second postulate can be stated as: Every dynamical variable may be ...
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### Vectors with more than 3 components

I have some confusion over Vectors, Its components and dimensions. Does the number of vector components mean that a vector is in that many dimensions? For e.g. $A$ vector with 4 components has 4 ...
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### Use of 'complete' as in 'complete set of states' or 'complete basis'

Question. In the context of QM, I hear the phrases 'complete set of states' and 'complete basis' (among other similar expressions) thrown around rather a lot. What exactly is meant by 'complete'? ...
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### How do you find a particular representation for Grassmann numbers?

This question is more general in the sense that I want to know how one finds a particular (say matrix) representation for any object. For the case of Grassmann numbers we have from Wikipedia the ...
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### Countable Matrix Representation

In my quantum mechanics class, my professor explained that the Hamiltonian along with position and momentum operators can be represented by matrices of countable dimension. This is especially usefull ...
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### These two operators commute…but their eigenvectors aren't all the same. Why?

The Hamiltonian $$H = \left[ \begin{array}{cccc} a & 0 & 0 & -b \\ 0 & 0 & -b & 0\\ 0 & -b & 0 & 0\\ -b & 0 & 0 & -a \end{array} \right]$$ commutes ...
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### How can (in Dirac's terminology) the product of two “real” linear operators be “not real”?

I'm puzzled about a statement from Dirac's book, The principles of quantum mechanics, (ยง8, p.28): As a simple examples of this result, it should be noted that, if $\xi$ and $\eta$ are real, in ...
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### Why superposition is useful just for linear functions?

I saw a problem which said that we have a bar between two walls and we increase the temperature. and as you know walls push a force to the bar so the length of it does not change. in the solution I ...
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### Finding all decompositions of mixed states

Some quantities, such as the entanglement of formation, are defined using a quantity that is minimized over all possible decompositions of a mixed state. A closed form can be found for this in some ...