Special types of matrices
In the world of matrices, some are so special that they have been singled out. Here they are.
Square matrices
A special type of matrix is a square matrix. A square matrix is one where the number of rows equals the number of columns. In other words, it is an m × n matrix in which m = n. Square matrices show up all over the place in quantum computing due to special properties that they can have—for example, symmetry, which is discussed later in the book. As we progress in the book, they will become one of the central types of matrices we will use. Some examples of square matrices are:
Identity matrices
An important type of square matrix is an identity matrix, named I. It is defined so that it acts as the number 1 in matrix multiplication so that the following holds true:
It has ones all down its principal diagonal and zeros everywhere else. Its dimensions need to change based on the matrix it is being multiplied by. Here are...