Special Matrices
- Column Matrix.or Column Vector. A matrix with only vertical
entries is called a column matrix, whose order is denoted by (m x 1). It
is a special case matrix with only one column.
- Row Matrix or Row Vector. A matrix with only horizontal entries
is called a row matrix, denoted by (1 x n). It is a matrix with only one
row and n columns.
Furthermore, a matrix with only 1 entry (scalar) would be both a column
and a row matrix.
- Square Matrix. A square matrix occurs when m=n or the number
of rows equals the number of columns. An example of a (3 x 3) matrix is:
- Identity Matrix or Unit Matrix.. This square matrix is of order
(n x n). The princpal (main) diagonal has all 1’s and the remaining elements
are all 0’s.
- Diagonal Matrix. Like the identity matrix all entries not on
the main diagonal are zero. Those entries on the main diagonal are not
restricted to 1.
- Symmetric Matrix. A square matrix is considered symmetric if
and only if it is equal to its transpose.
- Skew-Symmetric Matrix. A square matrix is skew-symmetric if
its negative is equal to its transpose.
A = 
- Triangular Matrix. Only square matrices can be considered upper
or lower triangular. A matrix is upper triangular if all its coefficients
below the main diagonal are all zero. Likewise, a matrix is lower triangular
if all its coefficients above the main diagonal are all zero. This property
can be used to find the determinant
of a matrix. An example of the upper triangular matrix is:
- Zero or Null Matrix. The zero matrix occurs when all elements
of a matrix are equal to zero. (Note: A zero matrix can be of various orders
and thus not all operations can be done on them.)
