There are several types of matrices that you should be familiar with. First, a square matrix is any matrix of dimensions. For example, the following matrices are square matrices of 2x2 and 3x3 dimensions respectively:  A diagonal matrix is a square matrix with zero or non-zero entries along the diagonal and zeros elsewhere. The following are 3x3 and 4x4 diagonal matrices:  An upper triangular matrix, usually denoted , is a matrix with zero or non-zero entries in and above the diagonal and with zeros elsewhere. The following are examples of a square 3x3 upper triangular matrix and a rectangular 3x5 upper triangular matrix: A lower triangular matrix, usually denoted , is likewise a matrix with zero or non-zero entries in and below the diagonal and with zeros elsewhere. One can also define strictly upper/lower triangular matrices in which the diagonals are also zeros but these find limited application in introductory coursework.

Finally, the identity matrix is a diagonal matrix with entries of 1 along the diagonal and zeros elsewhere. The following are 3x3 and 4x4 identity matrices:   Now that we have defined the basic mathematical objects of linear algebra, we will discuss the basic operations that can be performed on them in the following chapter.