A positive definite matrix 1 <p>Give any real symmetric or complex Hermitian positive definite \(2\times2\) matrix. Use integers or exact fractions for real and imaginary parts; enter %i for \(i\).</p><p>[[input:ansm]] [[validation:ansm]] [[feedback:result]]</p> <p>The checker uses Sylvester’s criterion to test positivity with exact arithmetic. Full credit requires both Hermitian symmetry and positivity. For real entries, Hermitian symmetry means ordinary symmetry.</p> 1 0.1 ansm matrix matrix([1,0],[0,1]) 1 0 1 1 1 1 result 1 1 0 PythonChecker ansm true {"checker": "is_hpd"} = 1 -1 spd-T = 0 -1 spd-F 1 ansm matrix([1,0],[0,1]) result 1 0 spd-T 2 ansm matrix([2,1],[1,2]) result 1 0 spd-T 3 ansm matrix([1/2,1/4],[1/4,1]) result 1 0 spd-T 4 ansm matrix([-1,0],[0,-1]) result 0 0.1 spd-F 5 ansm matrix([1,1],[1,1]) result 0 0.1 spd-F 6 ansm matrix([1,2],[0,1]) result 0 0.1 spd-F 7 ansm matrix([1,2],[2,1]) result 0 0.1 spd-F 8 ansm matrix([2,1],[0,2]) result 0 0.1 spd-F 9 ansm matrix([0,1],[0,0]) result 0 0.1 spd-F 10 ansm matrix([2,%i],[-%i,2]) result 1 0 spd-T 11 ansm matrix([1,%i],[%i,1]) result 0 0.1 spd-F 12 ansm matrix([1,2*%i],[-2*%i,1]) result 0 0.1 spd-F 13 ansm matrix([0,%i],[0,0]) result 0 0.1 spd-F 14 ansm matrix([1/2,%i/4],[-%i/4,1]) result 1 0 spd-T