Row Matrix
A row matrix is a matrix that consists of only one row.
The order of a row matrix is , where is the number of columns.
Its general form is:
For AI agents: use /llms.txt for the Nakafa content index.
A row matrix is a matrix that consists of only one row.
The order of a row matrix is , where is the number of columns.
Its general form is:
Example:
Matrix is a row matrix of order .
A column matrix is a matrix that consists of only one column.
The order of a column matrix is , where is the number of rows.
Its general form is:
Example:
Matrix is a column matrix of order .
A square matrix is a matrix that has the same number of rows and columns.
If , then the matrix is of order .
Its general form is:
In a square matrix, there are:
Main Diagonal (or Principal Diagonal):
The elements (i.e., where ).
Anti-diagonal (or Counter-diagonal):
The elements (i.e., where ).
Example:
Matrix is a square matrix of order . Its main diagonal elements are . Its anti-diagonal elements are .
A rectangular matrix is a matrix where the number of rows and columns are not equal ().
General example:
Matrix above has rows and columns, so its order is . Since the number of rows is not equal to the number of columns (), matrix is a rectangular matrix.
Rectangular matrices can be further distinguished into horizontal matrices and vertical matrices.
A horizontal matrix is a rectangular matrix with more columns than rows ().
Example:
Matrix is a horizontal matrix of order .
A vertical matrix is a rectangular matrix with more rows than columns ().
Example:
Matrix is a vertical matrix of order .
A triangular matrix is a square matrix where the elements below or above the main diagonal are zero.
An upper triangular matrix is a square matrix where all elements below the main diagonal are zero.
This means for every .
Example:
A lower triangular matrix is a square matrix where all elements above the main diagonal are zero.
This means for every .
Example:
A diagonal matrix is a square matrix where all elements outside the main diagonal are zero.
This means for every . Elements on the main diagonal can be zero or non-zero.
Example:
Matrix is a diagonal matrix of order .
An identity matrix (denoted by or ) is a diagonal matrix where all elements on the main diagonal are .
Example:
The identity matrix acts as the neutral element in matrix multiplication.
A zero matrix (denoted by or ) is a matrix where all elements are zero.
Example:
A symmetric matrix is a square matrix that is equal to its transpose ().
This means the element for all and . Its elements are symmetric with respect to the main diagonal.
Example:
In matrix :