Adjoint of Matrix
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Mathematics/Linear Algebra
Adjoint of Matrix Definition 1. Let A∈Mm×n(F)A∈Mm×n(F). We define the adjoint or conjugate transpose of AA to be the n×mn×m matrix A∗A∗ such that (A∗)ij=¯Aji(A∗)ij=¯¯¯¯¯¯¯Aji for all i,ji,j. Theorem 1 Theorem 1. Let A,B∈Mm×n(F)A,B∈Mm×n(F), and let C∈Mn×pC∈Mn×p. Then (a) (A+B)∗=A∗+B∗(A+B)∗=A∗+B∗ (b) (cA)∗=¯cA∗,∀c∈F(cA)∗=¯¯cA∗,∀c∈F. (c) $(AC)^* = C^*A^*..