Generalized quadraticity of linear combination of two generalized quadratic matrices

Değişmeli bir idempotent ve bir tripotent matrisin bazı lineer kombinasyonlarının alternatif karakterizasyonları

“…Considering (14) together with (1), (16), and (17) yields the following matrix equalities, respectively. ( 1 2 + 1 ).…”

“…There are a lot of studies related to these subjects in the literature. For details, it can be seen the references [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Matrices A such that A+1R = RA⁎ with R = I

“…Finally, we present the relationship between P R;s;k; and f 1 ; 2 ; : : : ; `gpotent matrices. The latter is an extension of the f 1 ; 2 g-quadratic matrices [22]. The set of all f 1 ; 2 ; : : : ; `g -potent matrices will be denoted by N f 1 ; 2 ; : : : ; `g .…”

On involutiveness of linear combinations of a quadratic matrix and an arbitrary matrix

“…In [1,2,4,7,13], it has been characterized the involutiveness of the form aA + bB when a, b ∈ C and A, B are special types of matrices. Moreover, there are a lot of studies related to the linear combinations including involutive matrices [4,7,9,14] and quadratic, generalized quadratic matrices [2,3,5,6,8,10,11]. These special types of matrices have applications to digital image encryption (for example, [12]).…”