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The term "adjoint maxtrix" is used for two different objects:
1) The transpose of the cofactor matrix (also called "adjugate matrix").
2) The matrix of the "adjoint operator" in an inner-product space: for an operator A and an inner product (x,y) the "adjoint" matrix A* satisfies (Ax,y)=(x,A*). In a real vector space, the adjoint matrix is the transposed matrix, in a complex vector space the adjoint matrix is the "Hermitian conjugate" (the transpose of the complex conjugate).
Eigen uses definition 2.
From: Listengine [mailto:listengine@xxxxxxxxxxxxxxxxx] On Behalf Of Luis Peñaranda
Sent: Wednesday, April 04, 2012 5:58 PM
Subject: [eigen] Adjoint
I am trying to compute the adjoint of a matrix, but Eigen 3.0.5 gives me a result I am not expecting. To illustrate this, I reduced the issue to the attached code. I understand "adjoint" as the traspose of the cofactor matrix.. In the attached example, the adjoint would be (checked with Maple):
-3 6 -3
6 -12 6
-3 6 -3
But Eigen gives me the transpose of my input matrix:
1 4 7
2 5 8
3 6 9
So the question is, does Eigen use another definition for adjoint, am I making a mistake in my code or is this a bug?
Thanks in advance for your answer,