/sci/ - Science & Math

>>11436973
Feel you. Altough I go to UU which is way worse. Litterally no one knows of it abroad and we are barely top 5 in Sweden.
Imagine applying for a job abroad with a degree from mediocre uni in a shithole country.

\begin{bmatrix}
1 & 0 & a \\
0 & 2 & b\\
0 & 0 & c
\end{bmatrix}

For what real values of a, b and c is this matrix diagonizable?
My answer is that for all choices of a and b if a != 2 and a != 1, if a = 2 or a = 1 then a=b=0 is the only choice. Otherwise the algebraic multiplicity will exceed the geometric.
Is this correct? Have I missed any cases?

Really stupid question but why and how does it work to translate a matrix into a vector.

Lets say I have 4 matrises that make up a basis in R4, I get that these have 4 dimensional vectors that are equivalent to each. But why can I just make a vector that consists of the entires on this from (M[1,1],M[1,2],M[2,1],M[2,2])^t ?