Linear Algebra question matrix multiplication

Mathematics
Tutor: None Selected Time limit: 1 Day

Which of the following may not be true for matrix multiplication even when the operations are defined?

a) Commutative

b) Associative

c) Multiplication is distributive over addition

Mar 1st, 2015

Please your answer is option a)

The algebra of matrices is not commutative, namely different operators don't commute each other, it is a fundamental characteristic of Quantum Mechanics.

In Quantum Mechanics the non-commutativity of the algebra of the operators, is expressed by the introduction of the commutator operator. Namely if I have two operators, represented by the matrices A, B, then the commutator operator is defined as follows:

[A,B] = A*B - B*A, which, of course is not equal to zero, in general. For example the commuattor between the operators coordinate and momentum is:

[x, p] = i* h/(2*pi), where i is such that i^2=-1 and h is the Planck constant, and pi = 3.14159...

Mar 1st, 2015

Are you studying on the go? Check out our FREE app and post questions on the fly!
Download on the
App Store
...
Mar 1st, 2015
...
Mar 1st, 2015
Dec 9th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer