Functions > Matrix Operations

Besides the functions available under this category, some other functions are also useful to work with matrices. These include the functions described in the category Numerical Manipulations and Number Theory and some of the functions described in the category Array and Data Manipulation.

The following functions are described in this section:

01. addcol | 02. addrow | 03. adjugate | 04. cofact |

05. columns | 06. comatrix | 07. delcols | 08. delrows |

09. det | 10. getcol | 11. getcolmatrix | 12. getiden |

13. getrow | 14. inverse | 15. inversedet | 16. isdiag |

17. isiden | 18. matrix | 19. minor | 20. minormatrix |

21. order | 22. rank | 23. ref | 24. rows |

25. rref | 26. trans |

Returns a new matrix by adding a new column. It has the following three forms:

**addcol ( matrix):**

Returns a new matrix adding one extra column filled with 0's at the right-most column of the given matrix.

**addcol ( matrix, index):**

Returns a new matrix adding one extra column filled with 0's at the specified index in the given matrix.

**addcol ( matrix, index, data):**

Returns a new matrix with one extra column at the specified

Returns a new matrix by adding a new row. It has the following three forms:

**addrow ( matrix):**

Returns a new matrix adding one extra row filled with 0's at the end of the given matrix.

**addrow ( matrix, index):**

Returns a new matrix adding one extra row filled with 0's at the specified index in the given matrix.

**addrow ( matrix, index, data):**

Returns a new matrix with one extra row at the specified

Expects a matrix as argument. Create a new matrix that is the adjugate (classical adjoint) of the input matrix.

Gets the **Cofactor** of a matrix for the specified row and column. Its syntax is:

cofact (*matrix, row_number, col_number*)

Returns the number of columns in a matrix.

Expects a matrix as argument. Creates a new matrix that is the **Matrix of Co-factors** for the specified matrix.

Returns a new matrix by deleting the given number of columns starting at the specified index. Its syntax is:

delcols (*matrix, index, count*)

Returns a new matrix by deleting the given number of rows starting at the specified index. Its syntax is:

delrows (*matrix, index, count*)

Expects a matrix as argument. Returns the determinant of the given matrix.

Retrieves the column at the specified index of a matrix as an array. It has the following form:

getcol(*a_matrix, index*)

Retrieves the column at the specified index as a column matrix. It has the following form:

getcolmatrix(*matrix, index*)

Gets an identity matrix with specified order. Its syntax is:

getiden (*order*)

Retrieves the row at the specified index as an array. It has the following form:

getrow(*matrix, index*)

Creates a new matrix, if defined, that is the inverse of the input matrix.

Creates a new matrix, if defined, that is the inverse of the input matrix. This functions uses the determinant and adjoint instead of the Reduced Row Echelon From used by the inverse function. The **inverse** function is more efficient and precise than this function. But it is given in case you need to calculate inverse based on the method of determinant and adjoint.

Expects a matrix as argument. Returns Boolean value 1 (i.e. true) if the argument matrix is diagonal. Returns 0 (false) otherwise.

Expects a matrix as argument. Returns Boolean value 1 (i.e. true) if the argument matrix is an identity matrix. Returns 0 (false) otherwise.

Creates a matrix. It can be called using either of the following two forms:

matrix (*array_1, array_2, ..., array_n*)

matrix (*value_1, value_2, ..., value_n*)

The arguments to the function matrix() are either single values or arrays of equal size. If single values are used, a column matrix is obtained. If arrays are used, they become rows of the resulting matrix. Arguments are processed from left to right while being added to the matrix from top to bottom.

The following commands show the use of matrix() function:

{ row1 = array (1,2,3): row2 = array (4,5,6): mat1 = matrix (row1, row2): mat2 = matrix( array(2,3,4), array(4,3,2)): }

Gets the **Minor** of a minor matrix for the specified row and column. Its format is:

minor (*matrix, row_number, col_number*)

Expects a matrix as argument. Creates a new matrix that is the **Matrix of Minors** for the specified matrix.

Expects a matrix as argument. Returns the order of the given matrix.

Expects a matrix as argument. Returns the rank of the given matrix.

Expects a matrix as argument. Gets the Row Echelon Form of the given matrix.

Expects a matrix as argument. Returns the number of rows in the given matrix.

Expects a matrix as argument. Gets the Reduced Row Echelon form of the given matrix

Expects a matrix as argument. Returns a new matrix which is transpose of the given matrix.