I'm working on a project to show linear algebras applications in electrical circuits. I don't have alot of experience with circuits, and I don't have any experience with differential equations, so I'm not quite sure how slim my options are.

 

Anyways, I've found out how to use augmented matrices to find loop currents, and now I've hit a wall so to speak. I've googled for ideas online but some are either too intense or not applicable. We're just starting eigenvectors, so I barely know how to work those. But if you can think of anything that I could expand on in my project given my circumstances, I would appreciate hearing them, thanks.

I don't have any knowledge of electrical engineering at all really. If you get ideas and are stuck on specific mathematical things then I might be able to help. I can certainly try to explain eigenvalues and eigenvectors if that might be of any use.

I don't have any knowledge of electrical engineering at all really. If you get ideas and are stuck on specific mathematical things then I might be able to help. I can certainly try to explain eigenvalues and eigenvectors if that might be of any use.

 

That time may come very soon, lol, and I appreciate your willingness to help

I don't really have much knowledge of electronics either but maybe try searching the 'Routh-Hurwitz' criterion on wikipedia. It involves finding the determinant of a matrix which is pretty simple. It determines the stability of mechanical systems but I think it works for electronic systems too.Also, nodal analysis matrices are very similar to loop matrices which you have already learned so maybe they are worth looking at..

 

And if all else fails try posting in the engineering forum, I'm sure some nice electronic engineer will help out...

I don't really have much knowledge of electronics either but maybe try searching the 'Routh-Hurwitz' criterion on wikipedia. It involves finding the determinant of a matrix which is pretty simple. It determines the stability of mechanical systems but I think it works for electronic systems too.Also, nodal analysis matrices are very similar to loop matrices which you have already learned so maybe they are worth looking at..

 

And if all else fails try posting in the engineering forum, I'm sure some nice electronic engineer will help out...

 

I appreciate the above ideas, and I'll search them out. I probably should have posted this in the engineering forum, but whats done is done, lol. I was actually looking at applications of matrices to nodes in circuits, but it confused me as the examples used arbitrary voltages and the given resistances to represent the different currents. I should be ok by tomorrow, the library will be open and I can continue my research there, but again I do appreciate the direction.

Anyways, I've found out how to use augmented matrices to find loop currents, and now I've hit a wall so to speak.

 

You generate systems of linear equations in resistive networks by doing mesh current analysis (as you have indicated above) and/or node voltage analysis.

 

Here's another nifty application. When dealing with sinusoidal inputs, dealing with the trigonometric functions can be a pain, especially when sines and cosines start cropping up in the same expression. To make life easier, electrical engineers often switch from the sine/cosine functions to complex exponentials. In linear algebraic terms, the set [math]\{\sin(kx),\cos(kx)\}[/math] spans the same vector space as the set [math]\{\exp(ikx),\exp(-ikx)\}[/math]. The switch from one set to the other is a change of basis.