# matrices

10. ### need some help with matrices

I have a 2 by 2 matrix ive figured out the A.B product, hopefully its right ;-; so ive got the answer 4 8 -8 10 now im just not sure how to figure out the inverse of A and how to solve A X + I = B thanks in advance.
11. ### Minimise difference between two matrices

Hello, I have been told that I need to minimise the error between two matrices, like so. {A_1}x = {A_2}s Where A_1 and A_2 are convolution folding matrices. x represents the desired filter and s the actual filter. I need to minimise the error between x and s. So using Cholesky, I would do...
12. ### Commutativity in the space of linear transformation on a 2D vector scape

A variant of a problem from Halmos : If AB=C and BA=D then explain why (C-D)^2 is commutative with all 2x2 matrices if A and B are 2x2 matrices. This result does not hold for any other nxn matrices where n > 2. Explain why.
13. ### Encoding matrices

Hi, I've got a question about 2x2 and 3x3 encoding matrices. Clearly, to receive whole numbers under matrix multiplication (encryption), you would need a matrix with the determinant of 1 or -1. However, what does it matter if you use a 2x2 or a 3x3 encoding matrix, as long as the determinant = 1...
14. ### Matrices Transformation

I would very much appreciate help with the following question: (i) Prove that the dot product of any two vectors u,v ∈ Rn is uTv. (ii) Given a Matrix A and vectors u,v ∈ Rn so that Au . Av = u . v , prove that A is orthogonal (for part (ii)we can assume that (AB)^t= B^t A^t)
15. ### Matrices

I cannot get my head around this question. I would very much appreciate any help please. If we are given invertible matrices A, B and P so that A = PB, we can say that A is ‘left equivalent to B’. Prove that ‘left equivalence’ is an ‘equivalence relation’.
16. ### Determinants and complex numbers

Hey everyone, Do you know if there are any links between the property of matrix determinants and Complex numbers. - a complex number being z=x+yi, where x and y are real numbers and i is the imaginary number which represents sqrt(-1) - a matrix being a 2x2 representation of a...
17. ### Matrices and Complex Numbers

Hey, So I'm studying the links between complex numbers and matrices at the moment, and have been using the matrix 0 1 -1 0 to express the complex number i, (which represents the square root of -1). I was wondering if there are any other ways to express i as a matrix?? Thankyou!! :)
18. ### Re: Linear Algebra-Transition Matrices

how to post the problem? Please, guide me
19. ### Linear Algebra-Transition Matrices

Hey guys, I'm after some help on this problem. Help would be much appreciated.
20. ### Showing that a set spans the subspace of symmetric matrices

I'm not really sure how to show this. It's the part about symmetric matrices that throws me off. What I know: A symmetric matrix has the property that A = A^T. To show that the set spans, I could create a matrix and show that if there are leading ones in each row, without a pivot in the...