I have a following block matrix
M1 =([a11 a12;a21 a22] [b13;b23];[b13;b23]' d33) + ([c -cr]'*[c -cr] 0;0 I)
now what i observe is that whether i use
[c -cr]'*[c -cr] or
[c cr]'*[c cr] (the sign change in
cr the eigen value of M1 doesn't change. How can i prove this in general? Or this is just a co-incidence that, with the examples i am running there is no change in eigen values of M1 with the sign changes.
Please I am really looking forward for your answers. Thanks in advance.
All the elements of M1 are matrices of appropriate dimensions.