Is the Matrix Positive-Definite?
C, 108 bytes

-1 byte thanks to Logern
-3 bytes thanks to ceilingcat



f(M,n,i)double**M;{for(i=n*n;i--;)M[i/n][i%n]-=M[n][i%n]*M[i/n][n]/M[n][n];return M[n][n]&gt;0&amp;(!n||f(M,n-1));}


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Performs Gaussian elimination and checks whether all diagonal elements are positive (Sylvester's criterion). Argument n is the size of the matrix minus one.