Understanding 2x2 Matrices: Representation and Dot Product

[Josh Conneely]

Homework Statement

Suppose a 2x2 matrix X (not necessarily hermitian, nor unitary) is written as

X = a0 + sigma . a (the sigma . a is a dot product between sigma and a)

where a0 and a1, a2 and a3 are numbers.

How on Earth does X represent a matrix? it's a number added to another number (dot product).

Homework Equations

The Attempt at a Solution

 

[Dick]

Homework Statement

Suppose a 2x2 matrix X (not necessarily hermitian, nor unitary) is written as

X = a0 + sigma . a (the sigma . a is a dot product between sigma and a)

where a0 and a1, a2 and a3 are numbers.

How on Earth does X represent a matrix? it's a number added to another number (dot product).

Homework Equations

The Attempt at a Solution

I suspect this is a question about Pauli matrices. That notation is shorthand for X=a0*I+sigma1*a1+sigma2*a2+sigma3*a3 where I is the 2x2 identity matrices and sigma1, sigma2 and sigma3 are 2x2 matrices collectively referred to as sigma. The result X is a 2x2 matrix.