This thing can be found using algorithms named for Danilevsky or Faddeev and Leverrier.
This function's roots for a bipartite graph are always real and positive. Two graphs are called cospectral if this entity for one of them is a scalar multiple of this entity for the other. This thing can be found using algorithms named for Danilevsky or Faddeev and Leverrier. When B can be written as P-inverse times A times P, this non-scalar entity is the same for B and A. If this function has no repeated roots, it is equal to the minimal (*) polynomial, and the entity used to generate it is diagonalizable. A given matrix is invertible if its corresponding one of these functions has a non-zero constant term. Applying this function to the corresponding matrix results in the zero matrix, according to the Cayley-Hamilton theorem. For a given matrix, this function equals the determinant of the matrix minus lambda times the identity matrix. For 10 points, identify this polynomial function of a given matrix, a function whose roots are the eigenvalues.
This function's roots for a bipartite graph are always real and positive.
characteristic polynomial