Types of matrices
Definition.A square matrix is a matrix in which the number of rows equals the number of columns (size n×n), the number n, is called the order of the matrix.
Definition.The zero matrix is a matrix whose entries are equal to zero, ie, aij = 0, ∀i, j.
Definition.Row vector is a matrix consisting of a one row.
Definition.Column vector is a matrix consisting of a one column.
Definition.Diagonal matrix is a square matrix whose entries standing outside the main diagonal are equal zero.
Example of diagonal matrix.
Definition.Identity matrix is a diagonal matrix in which all the elements on the main diagonal are equal to 1.
Denote.The identity matrix usually denoted by I.
Example of identity matrix.
Definition.Upper triangular matrix is a matrix whose elements below the main diagonal are equal to zero.
Example of upper triangular matrix.
Definition.Lower triangular matrix is a matrix whose elements above the main diagonal are equal to zero.
Example of lower triangular matrix.
N.B. The diagonal matrix is a matrix that is both upper triangular and lower triangular.
Definition.Specifically, a matrix is in row echelon form if:
Examples of row echelon form of matrix.
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