Cofactor() [2/2]

value_type Cofactor	(	size_type	iColumn,
		size_type	iRow
	)		const

Returns a cofactor associated with the specified element.

Parameters

iColumn	is an index of a column, where the element is located.
iRow	is an index of a row, where the element is located.

Returns

The cofactor of the element. If a summ of iColumn and iRow is even, the value is equal to the result of applying the Minor method with the same parameters. Otherwise the returned value is equal to the additive invertion of the Minor return value.

For any matrix \(A_{m\times n} = \left(\begin{array}{ccccccc} a_{1,1} & \cdots & a_{1,j-1} & a_{1,j} & a_{1,j+1} & \cdots & a_{1,n} \\ \vdots & \ddots & \vdots & \vdots & \vdots & \ddots & \vdots \\ a_{j-1,1} & \cdots & a_{i-1,j-1} & a_{i-1,j} & a_{i-1,j+1} & \cdots & a_{i-1,n}\\ a_{j,1} & \cdots & a_{i,j-1} & a_{i,j} & a_{i,j+1} & \cdots & a_{i,n} \\ a_{j+1,1} & \cdots & a_{i+1,j-1} & a_{i+1,j} & a_{i+1,j+1} & \cdots & a_{i+1,n}\\ \vdots & \ddots & \vdots & \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & \cdots & a_{m,j-1} & a_{m,j} & a_{m,j+1} & \cdots & a_{m,n} \end{array}\right)\)

A.Cofactor(i, j)

will calculate the determinant \({\left(-1\right)}^{i+i}\cdot \left|\begin{array}{cccccc} a_{1,1} & \cdots & a_{1,j-1} & a_{1,j+1} & \cdots & a_{1,n} \\ \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ a_{j-1,1} & \cdots & a_{i-1,j-1} & a_{i-1,j+1} & \cdots & a_{i-1,n}\\ a_{j+1,1} & \cdots & a_{i+1,j-1} & a_{i+1,j+1} & \cdots & a_{i+1,n}\\ \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & \cdots & a_{m,j-1} & a_{m,j+1} & \cdots & a_{m,n} \end{array}\right|\).

Exceptions

Chusov::Exceptions::InvalidParameterException

The current matrix is not square