On preserves on singularity and nonsingularity of matrices

• Autorzy: Kalinowski J.
• Języki publikacji: EN

Abstrakty

EN

Operators preserving singularity and nonsingularity of matrices were studied in paper of P. Botta under the assumption that operators are linear. In the present paper the linearity of operators is not assumed: we only assume that operators are of the form T = (fi,j), wherei,j : K -> K and K is a field, i,j is an element of {1,2,...,n}. If n > 3, then in the matrix space Mn(K] operators preserving singularity and nonsingularity of matrices must be as in paper of P. Botta. If n < 2, operators may be nonlinear. In this case the forms of the operators are presented.

Słowa kluczowe

EN

operators; matrices

PL

operatory; macierze

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 4
• Strony: 681--685
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Kalinowski J.

• Uniwersytet Śląski Instytut Matematyki, ul. Bankowa 14 40-007 Katowice, Poland,

Bibliografia

• [1] P. Botta, Linear maps that preserve singular and nonsingular matrices, Linear Algebra Appl. 20 (1978), 45-49.
• [2] C. K. Li, S. Pierce, Linear preserver problems, Amer. Math. Monthly 108 (2001), 591-605.
• [3] J. Kalinowski, Preservers of the rank of matrices over a field, Beitrage Algebra Geom. 50, 1 (2009), 215-218.