Linear Definition and 1000 Threads

I am currently enrolled in Multivariate Calculus and am looking to get build up a solid base of mathematics for undergraduate physics curriculum. I am looking for a Linear algebra book that will aid me in my quest. I currently own Axler's Linear Algebra Done Right, but I fear it is too...

Dear mechanical expert I have to realize a linear displacement system for a Hall sensor that has to slide along the central axis of a narrow cylinder and with which high intensity magnetic field measurements (1-14 Tesla) have to be made. The field is produced by a commercial vertical magnet...

I'm unsure what equation to use to achieve this. My solution was to draw a scale model and measure the distance offset from the bar and how relative that was to the same length bar bent to 90 degrees. My answer was 70.8% assuming a linear relationship between length of lever and force (is that...

I have a trouble showing proofs for matrix problems. I would like to know how A is invertible -> det(A) not 0 -> A is linearly independent -> Column of A spans the matrix holds for square matrix A. It would be great if you can show how one leads to another with examples! :) Thanks for helping...

I was reading about systems of linear equations. Even if we have the same number of unknowns and equations, we may still have infinitely many or no solutions. But if in addition to that the determinant of the matrix of coefficients does not vanish, then does it necessarily imply that we have a...

i get preparation for my university entering exam and i studying linear equation and they define it linear equation are those which graph line now my question is that why one variable linear equation called linear for example y=3 that actually give us just line why we draw line for this...

This is the exact definition and I've summarized it, as I understand it above. Why is it, that for elements in the third subspace, closure will be lost? Wouldn't you still get another vector (when you add two vectors in that subspace), that's still a linear combination of the vectors in the...

I read the Wiki page https://en.wikipedia.org/wiki/Electron_cyclotron_resonance as well as this answer here How does a cyclotron work? and it describes a setup where one has a cyclotron which has a static magnetic field pointing up through the dees and there is an alternating high voltage...

Hi all I am doing some research on High Frequency Linear Array beam forming (for imaging sonar). For that purpose, a linear Rx Array of 100 channels have been constructed with inter channel spacing of 14.3mm. A transmitting Tx probe operating at 420 KHz (approx. 300 cycles CW pulse) is placed...

I’ve been watching =AT2AcUch2CYj2r40rQ431p1Rt1SQ-YzVLo-ryJHYFIT8s9ZlMJ5pcWH9lN17FRuz2eLTlNPVb4fP2yk4PPLqjJK_6lpeWheAbATLZd7foljjUg2sOFxm-mZbhhcw3G9ApCzWIWNjgBGcGjoXMqdW6Jv-Rb8P2yA']https://www.youtube.com/watch?v=l3QQQu7QLoM What is the scientific name of the enigmatic long linear dark features...

Hi PF! I'm trying to find a 1D, linear, complex, 2nd order, eigenvalue BVP: know any that admit analytic solutions? Can't think of any off the top of my head. Thanks!

I have had a thought experiment in my head for a while now and I am unable to find clear enough examples/info that deal with similar issues, to solve it on my own. This is why I hope that someone in this forum can at least point me towards a solution or provide hints as to where should I be...

Summary:: Linear algebra 1.Let a a fixed vector of the Euclidean space E, a is a fixed real number. Is there a set of all vectors from E for which (x, a) = d the linear subspace E / 2. Let nxn be a matrix A that is not degenerate. Prove that the characteristic polynomials f (λ) of the matrix A...

Linear Motion Equation to get the common velocity of the block and bullet just after collision: v2=u2+2gs, I set v=0 at max height of s = 0.004 m and g = -9.81 m s-2 I got u = 0.28 m/s Then I calculate the impulse of the block using formula J = mv - mu, where v=0 and u=0.28 m/s and I got J = 1.4...

Hello, Please I need help to find the objective function of a linear program (attachement : example). I tried to figure it out from the formula provided in (attachement : formula) but I couldn't understand it, it's written (MIN(lambda)wj) I think it's the key to resolve my question ! ( Full file...

Hello, Please I need help to find the objective function of a linear program (attachement : example). I tried to figure it out from the formula provided in (attachement : formula) but I couldn't understand it, it's written (MIN(lambda)wj) I think it's the key to my question ! ( Full file is...

With the assumptions of Inviscid flow, no pressure gradient and no body force terms in 1-D Navier Stokes becomes 1-D nonlinear convection equation; And if we assume velocity of wave propagation is constant value c, equation becomes 1-D linear convection equation; This is online derivation and...

Hi, I have just joined the forum. Thank you all for being a part of such places so that people like me can get answers to the questions on their minds! --------------------------- I have been trying to understand how a quadcopter yaws. Referring to the figure below which is bird's eye view of...

Could I please ask for help regarding the final part of the following question: It is the very last part, to find v in terms of u. So I have that the velocity of the midpoint of XY is: V_m = (u/2) i + (u/2) j I let the position vector of P be: r_p = cos(wt) i + sin(wt) j (w = angular...

I use 2x -4 as the LCD and turn 8/(x - 2) - (13/2) = 3 into 16 - 13x - 4 = 3, I then get 12 - 13x = 3 which leads me to 13x = -9 so x = -9/13 which is the wrong answer. Where did I make a mistake?

Hello! I have some data of the form (x,y,z) which I know it is described by a function of the form: ##z=y(a+bx)##, where a and b are parameters to be fitted for. z and y have error associated to them while x doesn't (x is actually an integer going from 0 to 3 for each value of y). I tried to do...

Have I solved this linear approximation question correctly?

∈Was wondering if anyone here could help me with an explanation as to how Axler arrived at a particular step in a proof. These are the relevant definitions listed in the book: Definition of Matrix of a Linear Map, M(T): Suppose ##T∈L(V,W)## and ##v_1,...,v_n## is a basis of V and ##w_1...

My method is converting 14 into ##\frac {42} {3}, = \frac 7 3x## Then $$ \frac {126} { 21}, = 6$$

Ok, so to be honest I am not really sure to which subcategory this belongs, but I think it is high energy physics. So my question will be rather brief and vague , can you explain me the working principle of a linear transformer driver? Google wasn't of that much help with this one as it seems...

I don't know the terms so I'm sorry if the informations at summary above is unclear. But I add a detailed photo of my calculations below. I use Gauss' Elimination laws.

This is how I understand the torque (T1) created at the axis of rotation due to the spring would be calculated. This is considering the spring is starting from a fully extended state and is not already compressed. This is considering that (A) has a distance of 2 in. and the force from the spring...

Find the general solution of the ODE: $\check{X_1}=X_1$ $\check{X_2}=aX_2$ where $a$ is a constant.

Hi I am trying to learn optimal estimation by reading Gelbs Applied Optimal Estimation, and I am having hard time with finding \Gamma defined as the following: $$ \Gamma_k w_k = \int_{t_k}^{t_{k+1}} e^{F(t_{k+1} - \sigma)} G(\sigma) w(\sigma) d\sigma$$ Here F is a known matrix. So is G, and w...

hey so, this is an algebra assignment that we had to do and i really didn't understand the course material that well, but i managed to do the very first steps. anyways i was hoping you guys could help me finish the rest of this table. https://ufile.io/jowwrfj3 or you can see the file attached

Hello! I really don't know much about statistics, so I am sorry if this questions is stupid or obvious. I have this data: ##x = [0,1,2,3]##, y = ##[25.885,26.139,27.404,30.230]##, ##y_{err}=[1.851,0.979,2.049,6.729]##. I need to fit to this data the following function: $$y = a (x+0.5)/4.186 +...

Hi, I previously posted about the statically indeterminate truck problem. Thank you to everyone who helped me. However, I now realized that isn't the problem I need to solve. I need to know the force of the linear actuators to lift the rear tyres off the ground. Since the tyres will be...

The accompanying table lists the numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value of r. Determine whether there...

Hey! :o Let $1\leq n,m\in \mathbb{N}$, $V:=\mathbb{R}^n$ and $(b_1, \ldots , b_n)$ a basis of $V$. Let $W:=\mathbb{R}^m$ and let $\phi:V\rightarrow W$ be a linear map. Show that $$\ker \phi =\left \{\sum_{i=1}^n\lambda_ib_i\mid \begin{pmatrix}\lambda_1\\ \vdots \\ \lambda_n\end{pmatrix}\in...

attached resolution attempt

prove that $2+8{\sqrt{-5}}$ is unit and irreducible or not in $\mathbb Z+\mathbb Z{\sqrt{-5}}$.

prove that u(z+zw)={+1,-1,+w,-w,+w^2,-w^2}

W = {f(t) | f(0) = 2f(1)} The answer say yes, but i don't know how to prove the neutral element.

Let ##V## be a real vectorspace of finite dimension ##n##. Let ##L, K:V \rightarrow \Re## be linear transformations so that ##ker(L) \subset ker(K)##. Then there's a parameter ##\lambda \in \Re## so that ##K=\lambda L## a) Show that ##K=\lambda L## holds when ##K=0##. b) Suppose that ##K...

Hello everyone, I'm trying to make a hexapod table, in the same style as this: but I am trying to overcome the main flaw with this design - the minimum height being so high. My goal is to produce something which someone can stand on, in their home. It needs to become as flat as possible, and...

Hello I have these points coming from different experiments: ##x = [-0.3, -0.2, -0.09, 0.01, 0.2]## ##y = [-8.15, -5.20, -3.32, 0., 5.65]## ##y_{err} = [0.1, 0.27, 0.35, 0.09, 0.44]## and I need to fit a straight line to them (based on theoretical arguments). I attached below the obtained...

ok, setting the force issues aside (for now), Id like to use what I know about triangles to figure how to position my linear actuator in order to open and close this door correctly: The vertical side is 84cm, the door is 92cm. The measured stroke of the AL is 25cm. I would need to lower the...

I am trying to derive the adjoint / tangent linear model matrix for this partial differential equation, but cannot follow the book's steps as I do not know the math. This technique will be used to solve another homework question. Rather than posting the homework question, I would like to...

Hello! I have some data points obtained from a measurement and one of them is defined as the reference point. I need to compute the difference between that reference point and all the others (including itself) and plot the difference as a function of another variable (which doesn't have an error...

y''(x)+y'(x)+F(x)=0 Pleas me a idea

Hi ; I have a few question regarding the conservation of linear and angular momentum. Would appreciate any help. 1 - When no external forces act are both linear and angular momentum conserved in all 3 directions separately or just the total linear/angular momentum conserved ? 2 - if I approach...

Hi! This is a very simple question regarding terms of expressions. One law of motion is: F=ma Another, using L as the linear momentum, is: F = dL/dt If the first equation can be characterized (ignoring reference frames) as a "coordinate-based equation" (since is concerned with the second...

Hello folks, I am currently finishing up a class on linear algebra, covering vector spaces, bases and dimension, geometry of n-dimensional space, linear transformations and systems of linear equations. I am only getting accustomed to proof writing for the first time in this course. However, I...

Hello! I made a linear fit, ##y=ax+b##, to some data points and I get the best parameters with their (1 sigma) errors: ##a\pm\delta a## and ##b\pm\delta b##. I want to plot this fit on top of my data points in such a way as to reflect the error on the parameters. The "main" fit is simply...

At the start of Chapter 9, M. A. Armstrong in his book, "Groups and Symmetry" (see text below) writes the following: " ... ... Each matrix A in this group determines an invertible linear transformation f_A: \mathbb{R} \to \mathbb{R} defined by f_A(x) = x A^t ... ... "I know that one may define...