Tom M. Apostol in his book "calculus Vol. 2" page 122 (see image below) defines adjoint of a matrix as the transpose of the conjugate of the matrix. Is this definition always correct ? Does it agree with the adjoint defined here, i.e. transpose of the cofactor matrix?
Best Answer
These are two different concepts. The one that one hears a lot about is the usual adjoint of $A$, which is simply, as you say, the conjugate transpose of $A$, usually denoted by $A^*$.