Matrix Notation

12 Dec 2013

Matrix notation is a pain to deal with when writing in plain text/typing on a computer. There is another notation that may be easier to write and remember, especially if you're a programmer, as it uses braces to logically wrap rows and columns. Remember that matrices, rows take precedence, so they are always written first.

A 1 x 1 matrix looks like this:

{ Value1 }

A 2 x 2 matrix looks like this:

{{ Value1, Value2 }, { Value3, Value4 }}

A 3 x 3 matrix looks like this:

{{ Value1, Value2, Value3 }, { Value4, Value5, Value6 }, { Value7, Value8, Value9 }}

A 1 x 2 matrix looks like this:

{ Value, Value }

And a 2 x 1 (column vector) matrix looks like this:

{{ Value1}, { Value2 }}

In quantum computing, gates are often 2 x 2 matrices, and a qubit is represented by a 2 x 1 matrix, which is also known a column vector. In maths, any matrix that has only one column and many rows is considered a column vector.

We can also write our qubit state vector (the 2 x 1 matrix, or column vector) like this:

{ Value1, Value2 }^T

Raising the column vector to T denotes that we have rewritten the rows of our column vector as columns of our transposed vector.