Geodesic
An invariant of $2\times 2$ matrices
The electronic journal of linear algebra, Tome 13 (2005), pp. 146-152.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let W be the space of 2*2 matrices over a field K. Let f be any linear function on W that kills scalar matrices. Let A 2 W and define $fk(A) = f(Ak)$. Then the quantity fk+$1(A)/f(A)$ is invariant under conjugation and moreover fk+$1(A)/f(A) = trace$ SkA, where SkA is the k-th symmetric power of A, that is, the matrix giving the action of A on homogeneous polynomials of degree k.
Classification : 15A72, 15A69
Keywords: matrix invariants, power of a matrix, trace, symmetric power of a matrix 
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     title = {An invariant of $2\times 2$ matrices},
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Cisneros-Molina, José Luis. An invariant of $2\times 2$ matrices. The electronic journal of linear algebra, Tome 13 (2005), pp. 146-152. http://geodesic.mathdoc.fr/item/ELA_2005__13__a15/