10 Rings
... The importance of the distinction between algebraic integers and algebraic non-integers is perhaps still not clear. To understand this, we will first need some analogues of notions familiar from linear algebra. Definition 10.8. Let R be a subring of C. We say {αi } is a Z-basis for R if each αi ∈ R ...
... The importance of the distinction between algebraic integers and algebraic non-integers is perhaps still not clear. To understand this, we will first need some analogues of notions familiar from linear algebra. Definition 10.8. Let R be a subring of C. We say {αi } is a Z-basis for R if each αi ∈ R ...
2 Incidence algebras of pre-orders - Rutcor
... say it is c . The matrix M may have other non-zero entries. Consider the diagonal matrices Di and D j defined as in (5).We have M ij c.Di .M .D j and therefore M ij belongs to A( ) as claimed, concluding the proof that A( ) A . The two claims above being proved, the isomorphism stated in the ...
... say it is c . The matrix M may have other non-zero entries. Consider the diagonal matrices Di and D j defined as in (5).We have M ij c.Di .M .D j and therefore M ij belongs to A( ) as claimed, concluding the proof that A( ) A . The two claims above being proved, the isomorphism stated in the ...
ULinear Algebra and Matrices
... of A by the corresponding element in the jth column of B, and then add these products. The product matrix AB is an m k matrix. (The product AB of two matrices A and B can be found only if the number of columns of A is the same as the number of rows of B.) Example ...
... of A by the corresponding element in the jth column of B, and then add these products. The product matrix AB is an m k matrix. (The product AB of two matrices A and B can be found only if the number of columns of A is the same as the number of rows of B.) Example ...
