Determinants and Eigenvalues
Luz Maria DeAlba · 2006
The determinant , det A , of a matrix A = [ a i j ] ∈ F n × n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429138492/cc3be78c-f644-49c2-b40d-db06d778c1a5/content/eq598.tif"/> is an element in F defined inductively: det [ a ] = a . For i, j ∈ {1, 2, …, n }, the ij th minor of A corresponding to a ij is defined by m ij = det A ({ i }, { j }). The ij th cofactor of a ij is c ij = (–1) i + j m ij . det A = ∑ j = 1 n ( − 1 ) i + j a i j m i j = ∑ j = 1 n a i j c i j https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429138492/cc3be78c-f644-49c2-b40d-db06d778c1a5/content/eq599.tif"/> ofr i ∈ {1, 2, …, n }.