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Semidefinite programming can be regarded as an extension of linear programming. In a semidefinite program, the goal is to optimize a linear function over the intersection of the cone of positive semidefinite matrices with some affine space.
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how to determine a biquadratic form is positive-definite
A biquadratic form $\sum_{i,j,k,l}b_{i,j,k,l}x_{i}x_{j}y_{k}y_{l}$,
how to determine whether it is positive-definite?
A necessary and sufficient condition?
In fact, I have a matrix $B=\sum_{1\leq i …