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
Famous quotes containing the word block:
“The chess pieces are the block alphabet which shapes thoughts; and these thoughts, although making a visual design on the chess-board, express their beauty abstractly, like a poem.... I have come to the personal conclusion that while all artists are not chess players, all chess players are artists.”
—Marcel Duchamp (1887–1968)