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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Factoring positive semidefinite matrices over $\mathbb{Q}[i]$

Take the matrix $M_a$ with components $a=a,b=0,c=0,d=1$. Now the determinant is $a$. You would like that there is a matrix $A$ with coefficients in $\mathbb{Q}[i]$ and determinant $1$ s.t $$ A A^* $$ …
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