# Tagged Questions

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

152 views

### Tensors as multilinear maps

Sean Carrol's in his book on GR introduces tensors as a multilinear map of a set of dual vectors and vectors onto R. I usually think of tensors as a multidimensional array of numbers with fixed ...
508 views

### why non orthogonal states are indistinguishable?

I want to know what does it mean by distinguishable quantum state from Mathematics perspective I mean mathematically. As a non physics background student could any one explain me why non orthogonal ...
121 views

### Expanding a ket in the position basis?

My textbook says that to find the ket $|ψ\rangle$ in the same position basis as the ket $|ø\rangle$ we do the following: $$|ψ\rangle=\int dø|ø\rangle \langle ø|ψ\rangle$$ Firstly can $|ø\rangle$ be ...
109 views

128 views

### Prove that a translation operator times a reflection operator is unitary and Hermitian [closed]

I am trying to prove some properties of the product of the (unitary) translation operator $\hat{T}(a)\psi(x) = \psi(x-a)$ and the (Hermitian) reflection operator $\hat{R} \psi(x) = \psi(-x)$. In ...
34 views

696 views

### 2D - Kinematics - Linkage System using Vector Algebra [closed]

I have this question that I dont know how to solve correctly : My question is, how do I find $V_B$ ? I will find the angular velocities myself, but I want to know the method to get $V_B$ ? I know ...
1k views

### Physical applications of matrices and determinants

Other than notation devices, I don't see any direct application of matrices/determinants in physics. For example, they are just a different way to write a partial derivative and determinants find if ...
1k views

### 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 ...
153 views

### $\exp(i\alpha\hat {\bf n}\cdot{\bf \sigma} )=\cos\alpha I+i(\hat {\bf n}\cdot{\bf \sigma})\sin\alpha$

Could anyone tell me $\hat {\bf n}\cdot{\bf \sigma}$ is defined in such way? In the book they have not defined what is $n_z,n_x,n_y$. It is from Quantum Computing: From Linear Algebra to Physical ...
823 views

### Why consider only direction cosines?

Why are these called direction angles? Why do we consider only direction cosines and not direction sines or tans. What is its actual significance? And How to use them? Why are they called ...
421 views

147 views

### “Complete” confusion

The word "complete" seems to be used in several distinct ways. Perhaps my confusion is as much linguistic as mathematical? A basis, by definition, spans the space; some books call this "complete" -- ...
88 views

### The abstract space of metrics in GR

I know this is a general (har har) question, but has any work been done understanding the mathematical space the allowed metrics in GR form? (I guess it'd be called a tensor space???)
419 views

### Anybody have example of two-qubit non-Pauli and non-Clifford quantum gate?

A lot of known quantum gates are in the Pauli group (I,X,Z,Y) or in the Clifford group (H,P,Cnot). I need examples of the quantum gates that aren't in this groups. Also, are there are matlab functions ...
64 views

### 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 ...
134 views

### Kronecker sum or direct sum?

When we write $$H=\sum_k H_k$$ in condensed matter physics, are we using Kronecker sum or direct sum? I think this is direct sum. However, Wikipedia says it is Kronecker sum. Can anyone give some ...
545 views

### Non-symmetric Lorentz Matrix

I was working out a relatively simple problem, where one has three inertial systems $S_1$, $S_2$ and $S_3$. $S_2$ moves with a velocity $v$ relative to $S_1$ along it's $x$-axis, while $S_3$ moves ...
83 views

### Couple Masses - Change in Basis

I'm having trouble with the linear algebra used to solved a coupled mass problem. $\ddot{x}_1 = -(2k/m)x_1 + (k/m)x_2$ and $\ddot{x}_2 = (k/m)x_1 - (2k/m)x_2$ Shankar then sets the equation up in ...
3k views

### Applying angular velocity to a rotation matrix

I have a very simple question. In our project we store an object's orientation as a 3x3 matrix which holds the orthonormal base of that object's local space. For instance if the object is aligned with ...