# matrices's questions - English 1answer

31.989 matrices questions.

### Volume of a Hypercube After a Non-Linear Transformation

0 answers, 4 views matrices geometry transformation
Volume of a Hypercube After Non-Linear Transformation The volume of a hypercube can be derived from the determinant of the matrix with rows formed from the difference between one vertex of the ...

### How to derive the explicit formula for 2-dimensional recurrence relation $f(m,n)$?

I'm struggling to get the following recurrence relation into a closed form if possible: $$f(m,0)=f(0,n)=2$$ $$f(0,0)=0$$ $$f(m,n)=f(m-1,n)\cdot(2n+1)(2n+2) + f(m,n-1)\cdot(2m+1)(2m+2)$$ where $m$ ...

### 1 Can the matrix transpose be represented by $X^T = AXB$ for a given $A$ and $B$?

Can the matrix transpose be represented by $X^T = AXB$ for a given $A$ and $B$? I think it is possible, but please correct me if I am wrong--please see my attempt below. My thinking (not sure ...

### Normed vector space and convergence properties

Assume I want to the convergence of a sequence of matrices (finite dimension). Can I assume that the norm that I am working with is submultiplicative and the generalise with any norms saying that ...

### -1 Quadratic form using Lagrange methods

I need to find a new base where X1X2+X2X3+X3X4 Is the sum of squares( diagonal matrix) Im trying with Lagrange method but without success (row and column actions also accepted) If anyone can ...

### How to transform coordinate frame with given matrix?

0 answers, 26 views matrices transformation rotations angle

### Show that the entries of the square of diagonal matrix are equal to the square of the entries of the diagonal matrix.

The question seems trivial which is why I have some trouble coming up with a proof that is mathematically correct. BTW I cannot yet use eigenvalues as we have not yet covered them in class. If D=[...

### 1 Looking for a well-behaved distance/similarity measure of how close a matrix B is to the (pseudo-) inverse of a matrix A.

I have a two matrices, $A$ and $B$ with dimensions ($m$, $n$) and ($n$, $m$), respectively. I have an iterative machine learning algorithm (similar to a restricted Boltzmann machine) that changes the ...

### Question about eigenvalues of a matrix and powers and trace of a matrix

If $A^4$ has an eigenvalue $x$, say, does $A$ have an eigenvalue $y$ s.t $y^4=x$? I do not think this is true for all complex matrices but I cannot seem to find an example… Also, how do I prove that ...