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The main diagonal of a square matrix can be extracted in the Wolfram Language using Tr[m, List].

Given a matrix A, a Jordan basis satisfies Ab_(i,1)=lambda_ib_(i,1) and Ab_(i,j)=lambda_ib_(i,j)+b_(i,j-1), and provides the means by which any complex matrix A can be ...

Also known as "Laplacian" determinant expansion by minors, expansion by minors is a technique for computing the determinant of a given square matrix M. Although efficient for ...

The idiosyncratic polynomial is the bivariate graph polynomial defined as the characteristic polynomial in x of A+y(J-I-A), where A is the adjacency matrix, J is the unit ...

The characteristic equation is the equation which is solved to find a matrix's eigenvalues, also called the characteristic polynomial. For a general k×k matrix A, the ...

To solve the system of differential equations (dx)/(dt)=Ax(t)+p(t), (1) where A is a matrix and x and p are vectors, first consider the homogeneous case with p=0. The ...

A Tschirnhausen transformation can be used to algebraically transform a general quintic equation to the form z^5+c_1z+c_0=0. (1) In practice, the general quintic is first ...

A rewriting of a given quantity (e.g., a matrix) in terms of a combination of "simpler" quantities.

A fixed point for which the stability matrix has both eigenvalues negative, so lambda_1<lambda_2<0.

A fixed point for which the stability matrix has both eigenvalues positive, so lambda_1>lambda_2>0.