Recent content by simpleton

Hi all, Note: The text below is the motivation for my question. To jump to the question immediately, please skip to the line that says HI! I have a set of data points, let's call it A, and I ran principal component analysis to get the top 3 principal components to be able to represent the...

Hi, I would like to know, how do I evaluate the quality of correlation? Specifically, I have a set of N datapoints, each represented by k features. I want to know how the k features correlate with each other, and therefore, I created a k by k correlation matrix. I am using R-value, so the...

Hi HallsofIvy, Thank you very much for your reply! I understand now how the linear functions work. Could you help me with the second part as well? How do you prove that you can find a corresponding basis \{v_1...v_n\} exists given the basis of the dual space?

Hi, I'm learning about vector spaces and I would like to ask some questions about it. Suppose I have a vector space V, and a basis for V \{v_1, ... v_n\}. Then there is a dual space V^* consisting all linear functions whose domain is V and range is ℝ. Then the space V^* has a dual basis \{x_1...

Information is a form of energy?? Hi all, I recently read an article on economist about Maxwell's Demon. It is mentioned that someone disproved Maxwell's demon by considering the information you need to determine whether you should let the air molecule to go to the other side. This required...

Hi mrmiller1, Thanks for your reply. However, it seems that when I set error bars, the error bars for all the points will be the same. Is there a way for you to set different error bars for different points? Also, do you know a way to physically draw in the error curve or extreme line...

Hi all, I am trying to use excel to do error analysis. I have a set of data points, and I have the average value and standard deviation of all the data points (which I use to plot the error bars). I want to use the excel to plot the best fit line and extreme line to get the error. However, it...

Hmm ok. I think I understand it better now. The desired configuration is not symmetric. However, what we are doing is that we are superposing two symmetric situations (and therefore we can split the currents equally) to create the resultant asymmetric situation. Then we can easily get the...

Hi, I am still not really sure why all 3 vertices are equilpotential. If I do not connect the to the cube at points A and B, then I agree with you that by symmetry, the potential of all 3 vertices is the same. However, now you are connecting the cube resistor to a circuit at points A and B...

Hi all, Recently I came across a circuit problem: Consider a cube circuit, where there is a resistor on each of the edges (Thus there are 12 resistors in total). All resistors have resistance R. Find the effective resistance between any two adjacent points. I used the usual method of...

anyone?

Hi all, I recently learned about simple harmonic motion. In all the questions I have done, the springs are massless. I would like to know what happens when the spring has mass. I think that if the spring has mass, then the force in the spring will also have to counteract the weight of the...

In case you want to check your answer, the currents are 6/11 A, 17/11 A and 23/11 A respectively. You have to use both Kirchoff's Loop Rule and Current Rule. At least that's what I did.

What I mean is, say person A and person B note down the number of photons that hit them. When they compare their readings, will they differ? And if they do, who got hit more times?

Hi, I was reading on special relativity and was trying to understand it. However, I am still not very sure about the concepts. For example, I have this problem: I have 2 spaceships, A and B, traveling towards each other. Both have rest length x and speed v, where v is near the speed of...