ERIC Number: EJ774898
Record Type: Journal
Publication Date: 2007-Sep
Reference Count: 1
A Strange Property of the Determinant of Minors
Ajibade, A. O.; Rashid, M. A.
International Journal of Mathematical Education in Science and Technology, v38 n6 p852-858 Sep 2007
If M[subscript ij] are minors of an n x n determinant D with elements a[subscript ij] (1 less than or equal to i,j less than or equal to n), then we prove the following relationship [vertical bar]M[subscript k][vertical bar] = [vertical bar]D[vertical bar][superscript k-1]delta[subscript k] where M[subscript k] is any square sub matrix of order k of the matrix of minors M, delta[subscript k] is the determinant of a submatrix of D of order (n - k) taking the complements of the "row/column" positions that was used in M[subscript k], and 1 less than or equal to k less than or equal to n. The above relation generalizes the trivial case for k = 1 and is consistent with the proven relationship for k = n when delta[subscript n] is taken as 1.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
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