15 citations · 114 across the 30 of their papers we have counts for
6 papers · 1 filter
A Note on Quaternion Skew-Symmetric Matrices
Liqun Qi, Ziyan Luo
The product of a complex skew-symmetric matrix and its conjugate transpose is a positive semi-definite Hermitian matrix with nonnegative eigenvalues, with a property that each dist…
A Tensor Rank Theory and Maximum Full Rank Subtensors
Liqun Qi, Xinzhen Zhang, Yannan Chen
A matrix always has a full rank submatrix such that the rank of this matrix is equal to the rank of that submatrix. This property is one of the corner stones of the matrix rank the…
Generating Hypergraphs, Decomposability and Classification of Two-Step Nilpotent Lie Algebras
Shenglong Hu, Liqun Qi, Honglian Zhang
In 1973, Gauger proposed a generator-relation method and a duality theory for two-step nilpotent Lie algebras. Based upon these, he classified two-step nilpotent Lie algebras of di…
Nilpotent Decomposition of Solvable Lie Algebras
Liqun Qi
Semisimple Lie algebras have been completely classified by Cartan and Killing. The Levi theorem states that every finite dimensional Lie algebra is isomorphic to a semidirect sum o…
Three Minimax Ideal Relations of Lie Algebras
Liqun Qi
In this paper, we introduce near perfect ideals and upper bounded ideals, and study them as well as perfect ideals for finite dimensional Lie algebras. We show that the largest per…
On the M-eigenvalues of elasticity tensor and the strong ellipticity condition
Hua Xiang, Liqun Qi, Yimin Wei
Strong ellipticity is an important property in the elasticity theory. In 2009, M-eigenvalues were introduced for the elasticity tensor. It was shown that M-eigenvalues are invarian…