Maurice P

 10 Finding all inner products on $\mathbb{R}^2$ for which a given linear map is orthogonal 6 About the Fermat quotients with base $2$ 6 Elliptic curve formulas for point addition 4 How many numbers in a given range are coprime to $N$? 4 What causes the last item of the simple periodic continued fraction of the square root of positive prime to be double the first item?

### Reputation (2,128)

 +10 annihilator linear algebra +10 If $S$ and $T$ are commuting, normal operators, then $ST$ is normal +45 Which $\alpha$ such that $\alpha = T\epsilon_1$ for positive $T$? +15 Questions in section Linear Functional and Adjoints

### Questions (9)

 8 Existence of $n_1 \sigma(n_1) = n_2 \sigma(n_2) = \cdots = n_r \sigma(n_r)$ for any $r$ 6 Probability that the sum of $k$ distinct integers selected from $1, 2, \dots, n$ is divisible by $n$ 3 If $\cos p\alpha$ and $\cos q\alpha$ are rational with $p,q$ relatively prime, then $\cos \alpha$ is rational, or $\alpha$ is a multiple of $\pi / 6$. 1 How to simplify conditions for conjugations on $\Bbb C^2$ 1 Existence of $e$ such that there exist integers $x,y$ not both $0$ and that $\left|ax^2 + bxy + cy^2\right|\le e\sqrt{b^2 - 4ac}$

### Tags (115)

 61 linear-algebra × 90 12 inner-product-space × 2 23 matrices × 32 11 prime-numbers × 3 15 number-theory × 12 10 continued-fractions × 6 13 jordan-normal-form × 22 10 orthogonality × 2 12 elementary-number-theory × 11 9 congruences × 2

### Bookmarks (4)

 45 Is there a list of all typos in Hoffman and Kunze, Linear Algebra? 18 The product of two positive definite matrices has real and positive eigenvalues? 3 Product of symmetric positive definite matrices 0 Is a family of commuting self adjoint operators simultaneously diagonalizable?