Self doubt: what are eigen values of resultant matrix when add two matrices?

Question

if eigen values of matrix A = a,b,c
if eigen values of matrix B = x,y,z

then is it holds every time that eigen value of A+B = a+x, b+y, c+z ?

please give some reference to you answer, thankyou.

Answer 1

It's not true always because eigen values of [4 5] [2 1] are 6,-1 and eigen values of [9 -2] [-2 6] are 5,10 and when we add both the matrices it gives [13 3] [0 7] whose eigen values are 13,7 but if we add the eigen values of 1st matrix and 2nd matrix it gives the total of eigen values as 11,9.

And (sum of eigen values) 11,9 is not equal to the (sum of 2 matrices and then calculating it's eigen values) 13,7. Hence, proved it is not always true but in some cases it is true.