id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4706	Burqan, Aliaa; Dbabesh, Hamdan; Qazza, Ahmad; Khandaqji, Mona 	New bounds for the Eigenvalues of Matrix Polynomials	2023	13	.pdf	application/pdf	3958	370	94	REFERENCES 817 Finally, applying Lemma 4 to get w (H) ≤ w (S) ≤ 1 2 ( w (S11) + w (S22) + w (S33) + √ w2(S11)+}|S12∥2 + ∥S13∥2 + √ w2(S22)+}∥S21∥2 + ∥S23∥2 ++ √ w2(S33)+}∥S31∥2 + ∥S32∥2 Thus, w(H) ≤ 1 2 ξ + 2 cos2 ( π mn− 3 ) + 1 + √ ξ2 + ( 1 2 ( α+ η + √ (α− η)2 + 4β2 ))2 + τ2 + 2 + √ 5 4 + √( 2 cos2 ( π mn− 3 ) + 1 )2 + ( 1 2 ( α+ η + √ (α− η)2 + 4β2 ))2 + µ + √√√√(2 + √ 5 4 )2 + τ2 + µ. Conclusion We have established new effective bounds for the eigenvalues of matrix polynomials by employing the similarity of matrices and matrix inequalities including the numerical radius, spectral radius and matrix norms. Then w(T ) ≤ 1 2 n∑ k=1 w(Tkk) + √√√√√w2(Tkk)	cache/ejpam-4706.pdf	txt/ejpam-4706.txt