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In linear algebra and matrix theory, the Schur complement of a submatrix of a matrix is a matrix of the same size as its remaining subarrays, defined as follows: Suppose a (p + q)× (p + q) matrix m is divided into four parts a, b, c, d, divided. Proposition (schur complement condition): Let a ∈ r (m + n) × (m + n) a\in r^ { (m+n) \times (m+n)} be a symmetric matrix, write a in the block form [y m × m x x t z n × n] \left [ \begin {array} {cc} y_ {m. lmi / pages / schur complement in control Schur complement is an important tool in proving many lmi theorems. It is often used as a method for linearizing lmi.

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Schur complement is a tool for analyzing matrix block structures and has wide applications in optimization and control theory. Schur complement condition: Suppose a is a block symmetric matrix, which can be expressed as [a11, a12;

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