These are quick scribes from this really nice Lecture here by Maria Schuld.
We consider a measurement matrix which is a diagonal of measurement values and the corresponding probability assignments to each.
The expectation of such a random variable can now be represented in a quadratic form vector product such that for a vector , as
Quantum theory revolves around computing expectation of measurements and these ideas from classical linear algebra are extended in a general form as
in the most general case (can have non-diagonal elements as well) is a Hermitian matrix with eigen values equal to the measurements.
Playing in this world is all about manipulating via unitary matrices .
Different quantum computing models are polynomially equivalent.