Block Matrices
A positive 2n × 2n matrix may also be defined by blocks:
where each block is n × n. By applying the positivity condition, it immediately follows that A and D are hermitian, and C = B*.
We have that z*Mz ≥ 0 for all complex z, and in particular for z = ( v, 0)T. Then
A similar argument can be applied to D, and thus we conclude that both A and D must be positive definite matrices, as well.
Read more about this topic: Positive-definite Matrix
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