In similarity transformation, i . e . a product of an orthogonal matrix and a scalar matrix.
2.
A "'scalar matrix "'is a diagonal matrix which is a constant times the identity matrix.
3.
I am wondering how to prove that the casimir operator acts as a scalar matrix if the ground field is not algebraically closed.
4.
As the center of a matrix algebra or operator algebra is the scalar matrices, a-structure on the matrix algebra is a choice of scalar matrix a choice of scale.
Meaning
a diagonal matrix in which all of the diagonal elements are equal
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