# representation

1. ### What is the geometric mean (representation) of orthogonal matrices?

Could you explain the geometric mean (representation) of orthogonal matrices? The same question is for different types of matrices and also tensors.
2. ### Phasor Representation of sine wave

I don't understand why Sine wave should be represented as a phasor, that is, as a circle with a rotating vector. Why should it be rotating at angular speed (omega)? This is an additional item that confuses me. Suppose in the picture I am assuming it is moving at some speed; if it runs at twice...
3. ### tensor: outer product, representation, decomposition

It is given a tensor: $T=\begin{pmatrix} 1\\ 1 \end{pmatrix}\circ \begin{pmatrix} 1\\ 1 \end{pmatrix}\circ\begin{pmatrix} 1\\ 1 \end{pmatrix}+\begin{pmatrix} -1\\ 1 \end{pmatrix}\circ\begin{pmatrix} 1\\ -1 \end{pmatrix}\circ\begin{pmatrix} -1\\ 1 \end{pmatrix}$ 1) Why is it possible to write...
4. ### Color mixing representation in different Geometrical shapes.

Reference ...
5. ### Geometric representation of matrix transformation

I want to sketch the 2-vector \textbf{u}=\left( \begin{array}{c} 2\\ 3 \end{array} \right) and its image under the matrix transformation f: R^2\rightarrow R^3 defined by f(u)=\left( \begin{array}{cc} 1 & 0\\ 1 & -1\\ 0 & 1 \end{array} \right)\textbf{u}. Can I sketch both of \textbf{u} and...
6. ### An Anomaly of Decimal Representation

An Anomaly of Decimal Representation of Real Numbers 1/3=.333333333......... therefore 3(1/3)=1=.999999............... The resolution is that 1/3 \neq .33333....... Proof: If 1/3 = .333333..... then the open interval (0,1/3) has a largest member, which violates a fundamental axiom of the...
7. ### question about representation of spatial dimensions

Hi friends, I'm not on math field, but I have a question: it's possible to represent 3 dimensions in space using only 2 dimensions, but 1- is it possible to represent 2 spacial dimensions using only 1 dimension? 2- if it's not possible, why? Because people can represent a tesseract on 3d and...
8. ### Power Series Representation

Hello All, Work: I am trying to figure out a power series representation for the function shown in the attached image. I get to the point where I have two series representations that I would like to combine to one representation, but I am not sure how to go about doing that. It seems I begin...
9. ### Novel fractal inspired loop - Analytical or level set representation?

Hi all, I hope this is of interest to some of you and there is someone out there that is able to either provide an answer or direct me along the path to finding it myself. I will keep this to a length I hope is sufficient and necessary. BACKGROUND: I am an applied mathematician working part...
10. ### Decimal Representation and Expansion

Definition: Property at infinity: P_{\infty} =\lim_{n\rightarrow \infty} P_{n} You can't define a property at infinity without P_{n}. "Property at infinity" is convenient termijnology for the above definition; it does not mean a property evaluated at n=\infty, \infty is not a number...
11. ### Decimal representation is unique

.99..... and 1.00..... to n decimal places are not the same no matter what n is, but their difference approaches zero as n approaches infinity, just as the difference between any two n-place decimals in consecutive order does as n approaches infinity.
12. ### Power Series Representation of x*sin(x^2)

The power series representation of sin(x) is not hard to arrive at. The power series representation of x*sin(x^2), however, would be more difficult to compute because of the complexity of its derivatives. How would you use the power series representation of sin(x) to find the power series...

I did not realize how to use linear algebra to find the compact represebtation off(a)=a^{T}Qa-2b^{T}a+c Please show me the steps to this the example is from Linear and Nonlinear Programming By David G. Luenberger, Yinyu Ye...
14. ### matrix-vector representation for a system of ODE's

I am aiming to explicitly write the matrix-vector representation of this system. yâ€™1 = 5y2 - y1 + y3; yâ€™2 = 3y1 - y2 + t2; yâ€™3 = y3 - ty2 This is what I have so far: [ yâ€™1 ] [ -1 5 1] [ 0] [ yâ€™2 ] = [ 3 -1 0] [ t2] [ yâ€™3 ] [ 0 ? 1] [ ? ] Just not sure how...
15. ### simplest representation of the expression.

I have recently done a Karnaugh Map. Just click on the image and you will see it. I need someone to help me simplify it as I am struggling with it. Anyway this is the answer that I have written but I'm not sure it's right: gb' + gb +br'
16. ### parameter representation for non right curves

2.39 A canon bullet follows the curve : [x=50,0 t) [y= 78,4t - 4,9t^2] Lengths are in meters and time in seconds. The ground is horizontal and follows the x axis. A) Find position to the bullet in 1,0 seconds. I guess I find x[50,0*1 seconds = 50] Y= 78,4*1 - 4,9 * 1 ^2 = 78.4 - 24,01...
17. ### parameter representation

I am in the end of chapter two of three chapters in my math book. I have understood most of the chapter. But there is one thing I don't understand anything of and that is parameter representation. Task 2.34 A boat follows the curve given by [x = -2 + 3h] and [y = 9 - 4h] Lengths are in...
18. ### Representation of differential equation

Dear Forum Users: Given a system of differential equations in the form Eq1: x_1(t) + x_2'(t) + 2x_1(t)x_2'(t) = 2x_1'(t) Eq2: x_2''(t)x_1(t) + 2x_1(t)x_2'(t) = 3 I want to represent the situation where i replace x_2(t) in Eq1 by a known function \tilde{x}_2(t) and solve the resulting...
19. ### Power Series Representation

Using the power series representation for the function f(x)=1/(1-x) for |x|< 1, write f'(x) and f"(x) in terms of power series. Hence, show that (2x^2)/(x-1)^3 = summation of n from 1 to infinity [(n+1)n/x^n] for |x| > 1 The words "hence" there implies that the answer we found before hand...
20. ### Representation Theory

Let $g$ -> $U_g$ be an irreducible unitary representation of a finite group G in complex space X. If $e_ 1, \dots , e_m$ is orthonormed basis in X and $U_g$ = ($u_ij$(g)) is the matrix of operator $U_g$ in that basis, then M($u_ij$ conj $u_pq$) = dot product of $u_ij$ and $u_pq$ =...