In this paper, we construct matrix commutators involving hyperbolic functions [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and obtain some results related to the relation between these commutators and [Formula: see text].
Some results are obtained for matrix commutators involving matrix exponentials $\left(\left[e^{A},B\right],\left[e^{A},e^{B}\right]\right)$ and their norms.
Abstract:In this paper we rstly give majorization relations between the vectors Fn = {f , f , . . . , f n− },Ln = {l , l , . . . , l n− } and Pn = {p , p , . . . , p n− } which constructed with bonacci, lucas and pell numbers. Then we give upper and lower bounds for determinants, Euclidean norms and Spectral norms of Gram ma-
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