- 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.
- Inverse of a Matrix. Given two square matrices A and B. If A B = B A = I then A is said to be invertible and B is the inverse ofA.
- Symmetric Matrix. A square matrix is considered symmetric if and only if it is equal to its transpose.
- The following is an example of a (3 x 3) symmetric matrix:
- Skew-Symmetric Matrix. A square matrix is skew-symmetric if its negative is equal to its transpose.
- The following is an example of a skew-symmetric matrix:
A = 
- The diagonal terms of a skew-symmetric matrix must be zero.
- 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.)
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