Show that it is impossible to find a basis for the vector space ofn x n (n > 1) matrices such that each pair of elements in the basiscommutes under multiplication.
Show that it is impossible to find a basis for the vector space ofn x n (n > 1) matrices such that each pair of elements in the basiscommutes under multiplication.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Show that it is impossible to find a basis for the
n x n (n > 1) matrices such that each pair of elements in the basis
commutes under multiplication.
Expert Solution
Step 1
Basis: A basis is the set of vectors of the vector space V which is linearly independent and the set spans
the whole vector space V.
We know that the set of all the square matrices is the vector space under multiplication over the
field F.
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