I have a couple matrix or fixed-point looking questions. Let's say A is an invertible matrix, and we have the equation A*1 = 1, where 1 is the unit vector. Normally equations are based on the reverse of this, where given a known A, we want to determine the vector, but in my situation it's the other way around. Then, is the matrix A unique if it is invertible? Secondly, if this is true, does every invertible square matrix have a fixed vector? submitted by /u/RedditChenjesu [visit reddit] [comments ..read more

Let's say we have two vectors {1,1,1} and {0,0,0}, and two non-invertible matrices X and Y, following the equation XY{1,1,1} = {0,0,0}. If XY were invertible, then this statement wouldn't make sense, so I'm taking the case XY must be singular. Now suppose X and Y are each decomposable into an invertible matrix A multiplied by a diagonal and non-invertible matrix D, such that we have (A_1*D_1) * (A_2*D_2) {1,1,1} = {0,0,0}. At this point the only matrices that could possibly be non-invertible are D_1 and D_2. Is (A_1*D_1)(A_2*D_2) or either sub component A_1D_1, or A_2D_2, necessarily the zero ..read more

Let's say we have to bounded linear transforms A and B. Let's say we know the spectra of A and B. Is there then anything that can be said about the spectrum of A*B? If not, then let's say we have two matrices A and B. Is there anything that can be said about the spectrum of A*B? I didn't see many results on this. Still too specific? No known theorems? Okay, what if A is invertible and B is diagonal, but singular. Now is there anything that can be said about the spectrum of AB? submitted by /u/RedditChenjesu [visit reddit] [comments ..read more

Hey everyone! I will need some help for my course on mathematics models I need books, videos or anything helpful on these subjects: Dimensional Analysis, A potential for chemical bonds, Dynamics of Vortices and Charges, Population Models, Euler-Lagrange equations. Thanks a lot! submitted by /u/sokspy [visit reddit] [comments ..read more

For two matrices A and B multiplied together as A*B*A, B is invertible, but A is not though A is diagonal. In the particular case that one as ABA{1,1,1} = {0,0,0}, where ABA together must be non-singular, is there anything in particular I can efficiently infer about the structure of ABA (or A?) based on known entries of B, but unknown entries of A? For instance, can I assume one possibility is that ABA is the zero matrix? Can I assume ABA is a matrix of explicit, particular constants with one degenerate row? Or two linearly dependent rows? Can I assume A is a matrix of zeros? Is there any inf ..read more

Hi everyone. I'm a second year math major and so far I really liked learning about logic and proofs in my discrete mathematics course. I also really like calculus. What fields would be good to go into with those interests? submitted by /u/anonymoususer666666 [visit reddit] [comments ..read more

There's taylor series for square roots, but, is there also an infinite *product* of polynomials of a particular variable? submitted by /u/RedditChenjesu [visit reddit] [comments ..read more

As far as I remember, if you have two invertible matrices A and B, then the product AB is invertible. But I'm considering a different scenario, I want to know, beginning with "what if AB is not invertible?" then what is the result? Is the result that if AB is non-invertible, then either A or B is not invertible? submitted by /u/RedditChenjesu [visit reddit] [comments ..read more

So, I am always trying to make my dishwasher packing more efficient, and my habit off putting mugs and glasses together on the top has reminded me of reading about the circle packing algorithms when I was younger. I believe we've solved situations for infinite planes with circles of the same size, but where else have we explored this. Are solutions in finite space with differing radius for the circles trivial? And yes, I know my dishwasher is 3D and a different situation, bit it's what triggered the curiosity. submitted by /u/TorbenSH [visit reddit] [comments ..read more

Im just a 20yr old looking for some direction in choosing a right path for my future. I am currently looking to do BSc. Mathematics in Germany and I want to know if it is a good option or not! And how hard can BSc. Mathematics be in general! Im really fond of numbers and the wonders they do. I want to keep both the paths of engineering and economics open after I do my Bachelors so im thinking BSc. Mathematics might be a good option. It would be great if you shed your experienced light on it. submitted by /u/_jaydevd_ [visit reddit] [comments ..read more