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Computer Arithmetic and Validity
book

Computer Arithmetic and Validity

by Ulrich Kulisch
April 2013
Intermediate to advanced content levelIntermediate to advanced
456 pages
16h 7m
English
De Gruyter
Content preview from Computer Arithmetic and Validity
Section 2.2 Vectoids 59
Once again let us consider matrices over a given ringoid R. In addition to the inner
operations and the order relation defined above in M
mn
R, we now define an outer
multiplication by
^
a2R
^
.a
ij
/2M
mn
R
a .a
ij
/ :D .a a
ij
/.
Then the following theorem holds.
Theorem 2 .12. Let fR, C, g be a ringoid with the neutral elements o and e.Then
fM
mn
R, Rg is a vectoid. The neutral element is the matrix all components of
which are o.IffR, C, , g is a weakly ordered (resp. an ordered) ringoid, then
fM
mn
R, R, g is a weakly ordered (resp. an ordered) vectoid.
Proof. We omit the proof of this theorem since it is straightforward.
For m D 1 we
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Publisher Resources

ISBN: 9783110301731