ABSTRACT
We know that there are matrices that cannot be diagonalized. However, there is a way to almost diagonalize all complex matrices. We now develop this somewhat long story.
There are matrices that can be considered the basic building blocks of all square complex matrices. They are like the prime numbers in N. Any n ∈ N is uniquely a product of primes except for the order of the prime factors that can be permuted. An analogous fact holds for complex matrices. The basic building blocks are the Jordan blocks.
