A Note on k‐Commutative Matrices

A note on positive deniteness and stability of interval matrices

It is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness and stability of interval matricescan be presented. These conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.Furthermore we introduce a new necessary and sucient condition for checkingstability of interval...

A note on positive deniteness and stability of interval matrices

It is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness and stability of interval matricescan be presented. These conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.Furthermore we introduce a new necessary and sucient condition for checkingstability of interval...

A note on companion matrices

We show that the usual companion matrix of a polynomial of degree n can be factored into a product of n matrices, n− 1 of them being the identity matrix in which a 2 × 2 identity submatrix in two consecutive rows (and columns) is replaced by an appropriate 2 × 2 matrix, the remaining being the identity matrix with the last entry replaced by possibly different entry. By a certain similarity tran...

A Note on Nilpotent Lattice Matrices

Some properties and characterizations for nilpotent matrices are established and in particular, a necessary and sufficient condition for an n × n nilpotent matrix to have the nilpotent index 2 and 3 is given. Mathematics Subject Classification: 15A33; 06D99

A note on power bounded matrices