Dictionary:Determinant

{{#category_index:D|determinant}} A scalar function of a square matrix (A):

${\text{det}}{\textbf {A}}=\sum _{i}a_{ik}A_{ik}=\sum _{k}a_{ik}A_{ik}$,

where A_ik is the cofactor of the element a_ik. The cofactor is $(-1)^{i+k}$ times the matrix found by deleting the ith row and the kth column of the original matrix $A$. The expansion is often called the expansion into minors of the determinant.