Is a matrix formulation of Fourier series meaningful and possible?

Narasim Ramesh @Narasim_Ramesh2

07 July 2015 1 6K Report

Consider a 2 dimensional real m*n matrix [ A] . Is it possible to express this

as [ A] = [ A0] + [ A1] *sin(theta) +... [ Ak] *sin(k*theta) ....

..where sin(k*theta) is a scalar.

Narasim Ramesh

A trivial example is the rotation matrix A=[ cos(theta) -sin(theta) ; sin(theta) cos(theta)]

A= Z+ cos(theta) *I +sin(theta)* J where Z= zero matrix, I =identity , J =[ 0 1 ; -1 0]. So obviously one can construct such matrices but is it true that any matrix can be decomposed in this fashion needs an answer.

Cheers

Badges
Science topic

More Narasim Ramesh's questions See All

Does SVD reflect accurately the user ratings and movie classification?

A simple example is explored in attached pdf by building a matrix a with given user rating and movie claasification and weights , but we do not seem to recover our original data components , hence...

04 May 2019 9,949 4 View

Is it possible to estimate hotness of chile by visual inspection?

Often it is difficult to add the correct number of chiles in cooking so that required taste is obtained . Estimating the hotness ( Scoville Heat Unit ) would help in meeting targetted taste. It...

11 December 2018 8,581 6 View

How to design a basic introductory course in AI for Ug?

AI requires facility in Linear Algebra,ANN, Calculus ,Probability and RP(Bayesian rules), DSP, Image processing ,NLP and programming. What would be the bare essentials(foundation) from these...

10 November 2018 657 9 View

Are there smooth elegant functions which are aperiodic ?

Here is an excerpt from Schroedinger's "What is life?" Would be interesting to view this mathematically using smooth ordinary type functions ,which are not spliced and joined. Schroedinger...

05 June 2018 8,977 4 View

Will every closed curve have foci determined by some criteria?

We can think of the circle center as a "focus" of points of its circumference given by distance to center = constant. In case of an ellipse we have sum of distance from points on boundary to the...

01 February 2018 2,743 9 View

Are there mathematical functions to describe the shapes of various biological objects, especially anthills?

There seem to be a wide variety of shapes in the biological world . In 2d we have various shapes of leaves. In 3d we have anthills , trees , fruits and animals with different shapes. All of them...

01 February 2018 6,295 19 View

What is the intuition to construct link and cannot link projection matrix?

In Power system islanding Dimension reduction is obtained for the Lyapunov Matrix via link and do not link on generator nodes . It would be helpful if a numerical example giving a clear picture of...

05 June 2017 6,021 0 View

Does evolution imply a higher form of "consciousness" which is non biological?

Darwin's theory of evolution shows that life forms adapt to new situations. This leads to following questions : 1. What is the primary cause of change in situations in the world? Even with the...

31 December 2016 7,850 4 View

How can we explain impact of green and new ethical challenges to ug electrical engineers.?

Technology has progressed in a manner which brings in may disciplines together. As an example Gene editing will require sensing / simulation/ electrical/chemical/ mechanical inputs . In what way...

05 June 2016 1,509 2 View

How do coconut trees get so much water up above the ground ?

It is interesting to observe coconut trees which transport water from the ground(?) to fairly large heights .What is the mechanism ? Can we replicate it artificially? .Why should it grow so tall...

04 May 2016 4,971 8 View

What is the difference between mathematical R^4 space and physical 4D unit space?

We assume that the difference is huge and that it is not possible to compare the two spaces. The R^4 mathematical space considers time as an external controller and the space itself is immobile in...

10 August 2024 6,678 14 View

Geotechnical Engineering (Proceedings of the ICE) time review?

Hello everyone, I recently submitted an article to Geotechnical Engineering (Proceedings of the ICE), and the current status has been listed as "EiC Pre-assessment: Ready" for the past 20 days. I...

10 August 2024 6,493 1 View

How to define an anisotropic material with asymmetric elastic compliance/stiffness matrix in ANSYS APDL?

I need to model an anisotropic material in which the Poisson's ratio ν_12 ≠ ν_21 and so on. Therefore, the elastic compliance matrix wouldn't be a symmetric one. In ANSYS APDL, for TB,ANEL...

09 August 2024 5,048 2 View

Can we mark 'EFL Learners shifting from general digital to AI technologies' as technological transition?

After COVID-19 it has seen that EFL learners technological affiliation has raised. In addition, in the post-COVID period learners started to engage AI technologies like ChatGPT while learning...

08 August 2024 8,964 4 View

Is it true that $\det(V(A))$ may be only $\pm 1$, depending on $n$, for the last symmetric tridiagonal matrix $A$?

One can try to generalize the Vandermonde determinant in the following direction: Let $A$ be any symmetric $n$-order square matrix. Consider its powers' diagonal elements $(A^k)_{ii}$ and...

08 August 2024 6,690 1 View

How does grain and grain boundary affect the ceramic when studying its dielectric properties?

I am not able to get good literature and the physics behind how first these grains and grain boundaries arises out of no where when we make a pellet to study its dielectric properties and then how...

07 August 2024 5,177 3 View

Usage of internal standards in LC-MS/MS analysis?

Have you ever seen a LC-MS/MS method uses both internal standards and external standards (in matrix matching purpose) but the concentrations of internal standards are outside the calibration curve...

05 August 2024 3,084 6 View

Why is the molecule's orientation with an electric field affect polarizability?

Why is the molecule's orientation with an electric field affect polarizability? Electrons are diffuse enough to be independent with respect to orientation and effect of electric field on...

03 August 2024 7,843 1 View

Request a single Lecture notes for math as detailed as this that I can find in one place?

- The Existence/Uniqueness of Solutions to Higher Order Linear Differential Equations - Higher Order Homogenous Differential Equations - Wronskian Determinants of $n$ Functions - Wronskian...

03 August 2024 2,366 0 View

Should I remove an item from a scale to raise Cronbach's alpha and McDonald's omega or is it better to leave it if they are both over .7 already?

Hello! I have this scale which had 10 items initially. I had to remove items 8 and 10 because they correlated negatively with the scale, and then I removed item 9 because Cronbach's alpha and...

01 August 2024 4,606 7 View