Questions tagged [linear-algebra]
To be used for linear algebra, and closely related disciplines such as tensor algebras and maybe clifford algebras.
1,140 questions
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Why would the normalisation of a vector with 2 complex numbers only give us 3 real parameters?
If a general spin state is characterised by 2 complex numbers, that would mean that 4 real parameters characterise it. I'm assuming that they are given by the complex and real parts of said complex ...
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Why use the QR factorization method to diagonalize a matrix? Considering better alternatives
Last year, I took a course in Computational Physics, where I learnt methods to integrate and differentiate functions, diagonalize matrices, etc. More precisely, I recall we would diagonalize matrices ...
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Why to maintain the equality of a matrix when we transposed it, we have to, not just interchange the order of the indexes, but also their height? [duplicate]
I was watching this videos series introduction to relativity: https://youtu.be/J1Ow27qFc18?list=PLeoh1MW56PeLn-tYxepNXBnfTMdbBemfJ&t=1850 and he was explaining how to found an implicit matrix ...
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Sum of three distinct frequencies equal zero
I am reading Feynman lectures (https://www.feynmanlectures.caltech.edu/II_33.html) and trying to understand the reflection of light from a boundary. To arrive at the transmitted and refracted ...
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Instantaneous eigenstates and real solutions of Schrödinger Equation [closed]
As we know, instantaneous eigenstates of energy are the states in which the wavefunction collapses instantly after we measure energy. And we also know that instantaneous eigenstates don't satisfy the ...
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Reflectogram deconvolution via bilinear forms
I work with highly coherent laser light 1550 nm source traveling through singlemode fiber. EOM creates laser pulses ~100 ns length corresponding to $m\approx 10$ m length of pulse. I can tune laser ...
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Ordering of Eigenvalues when Solving Coupled Oscillator Problem
First time posting here.
I'm working on solving a coupled oscillator problem with 3 blocks. Heres a quick drawing:
I'm assuming no friction, ideal springs, etc. Each block has mass $m$ and every ...
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What kind of subspace is this?
(Original title "When is a subspace called real?" was changed after discussion)
This is perhaps partly about math terminology, but the situation often occurs in physics so I'd like to know ...
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How does index notation work in complex vector spaces with non-degenerate Hermitian forms?
My experience with index notation is strictly in the context of special relativity where the real vector space $V$ is equipped with a symmetric, non-degenerate bilinear form $g:V\times V\to \mathbb{R}$...
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Mathematicians’ vs. Physicists’ Perspective on Vector Components [closed]
This is how I believe the argument should be presented to a first-year physics student.
In a nutshell, physicists tend to view a vector as an $n$-tuple characterized by its transformation properties, ...
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Index order in Einstein notation [duplicate]
I am learning about four-vectors in special relativity in my electrodynamics lecture.
We have learned that under Lorentz transformations $\Lambda$, vectors transform like
$$
x'^{\mu} = \Lambda_{~~~\nu}...
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Geometric Objects and Vector Functions
I'm Reading a Tensor analysis Book. In which it is Written that R=R(Z). The R in Left hand side of the equation is the "Geometric Object" in space which doesn't depend on a co-ordinate ...
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A vector is something that transforms like a vector
Inspired by this good answer Conceptual difference between covariant/contravariant (by Paul Frost), I would like to place on solid mathematical footing the physicists’ notion of contravariant and ...
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How can eigenvalues be used to determine attitude stability in rocket flight? [closed]
I am aware of the linearization of ODE's and their link with eigenvalues where you are able to solve coupled differential equation problems utilising eigenvalues and vectors. Additionally, I ...
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Is the symmetry of a system self-adjoint?
Say we have the statement;
An observable $A$ is a symmetry of the system if $[A,\hat H]=0$ where the Hamiltonian doesn't explicitly depend on time.
We now know that $A\hat H = \hat H A$
does this ...
