# Hu Zhengtang

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 12 Show that the matrix $A^2 + I$ is invertible for all matrices $A$, where $A$ is an $n \times n$ symmetric matrix. 10 Prove that if $\int f^2$ and $\int( f'')^2$ converge, so does $\int (f')^2$ 9 Prove that 360 divides (a-2)(a-1)a.a.(a+1)(a+2) 7 Show that $A$ is symmetric, with $A \in M_n(\mathbb R)$ 7 How prove this inequality $\sin{\left(\dfrac{\pi}{2}ab\right)}\le\sin{\left(\dfrac{\pi}{2}a\right )}\sin{\left(\dfrac{\pi}{2}b\right)}$

# 3,218 Reputation

 +10 Are there sometimes only finitely many square roots of a positive matrix? +10 Show that $A$ is symmetric, with $A \in M_n(\mathbb R)$ +10 Prove $f(x)=ax+b$ +10 How prove this inequality $\sin{\left(\dfrac{\pi}{2}ab\right)}\le\sin{\left(\dfrac{\pi}{2}a\right )}\sin{\left(\dfrac{\pi}{2}b\right)}$

# 2 Questions

 4 Is the inverse of an invertible totally unimodular matrix also totally unimodular? 2 Infimum over area of certain convex polygons

# 55 Tags

 45 linear-algebra × 11 19 integration × 5 39 matrices × 7 18 sequences-and-series × 4 32 real-analysis × 17 16 inequality × 6 28 complex-analysis × 14 14 elementary-number-theory × 3 19 calculus × 5 12 analysis × 6

# 2 Accounts

 Mathematics 3,218 rep 217 MathOverflow 101 rep 2