The sum of the eigenvalues of two matrices A and B, specifically 2x2 matrices, equals the sum of their individual eigenvalues. This property holds true due to the linearity of the trace function, which states that the trace of a matrix (the sum of its eigenvalues) is additive. Therefore, for matrices A and B, the equation tr(A + B) = tr(A) + tr(B) confirms that the eigenvalues of A+B are simply the sum of the eigenvalues of A and B.
PREREQUISITESStudents studying linear algebra, mathematicians, and anyone interested in the properties of eigenvalues and matrix operations.
Since you solved this problem, then you should know why this is so.tatianaiistb said:Homework Statement
I solved a problem that asked me to show that the sum of the eigenvalues of A+B equals the sum of all the individual eigenvalues of A and B, and similarly for products. I just would like to know why is this so...
tatianaiistb said:Homework Equations
The Attempt at a Solution
Is it because we're combining A and B?