But, if it is, then

(X' Y' X Y) (Y' X' Y X) = X' ( Y' ( X (YY') X' ) Y ) X = the identity = I

Also (XY) (XY)' = I = X Y Y' X' => (XY)' = Y'X'

Bob

]]>hi pi_cubed

I tried X and Y as 2 x 2 matrices, just making up some numbers. I didn't get the same answer evaluating X' Y' X Y and Y' X' Y X. It was a long calculation so I may have slipped up of course.

Did you just randomly make up the relationship, or does it come from something?

Bob

I think I read an article somewhere about it but I might have remembered it wrong.

]]>I tried X and Y as 2 x 2 matrices, just making up some numbers. I didn't get the same answer evaluating X' Y' X Y and Y' X' Y X. It was a long calculation so I may have slipped up of course.

Did you just randomly make up the relationship, or does it come from something?

Bob

]]>pi_cubed wrote:I think the group theory relationship in my signature is flawed.

What does an group theory relationship mean?

In mathematics and abstract algebra, **group theory** studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.

Various physical systems, such as crystals and the hydrogen atom, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.

The early history of group theory dates from the 19th century. One of the most important mathematical achievements of the 20th century was the collaborative effort, taking up more than 10,000 journal pages and mostly published between 1960 and 1980, that culminated in a complete classification of finite simple groups.

pi_cubed thinks his signature is flawed.

]]>I think the group theory relationship in my signature is flawed.

What does an group theory relationship mean?

]]>ganesh wrote:Many years ago, I declared:

Sum of two cubes in two different ways (resulting in a sum which is a positive number) is 91.

Cubes numbers can be both positive and negative, aren't they?Interestingly,

is zero.Trivial!

What do you mean by n^3 and -n^3 is zero?

I meant sum.

]]>Many years ago, I declared:

Sum of two cubes in two different ways (resulting in a sum which is a positive number) is 91.

Cubes numbers can be both positive and negative, aren't they?Interestingly,

is zero.Trivial!

What do you mean by n^3 and -n^3 is zero?

]]>Sum of two cubes in two different ways (resulting in a sum which is a positive number) is 91.

Cubes numbers can be both positive and negative, aren't they?

Interestingly,

is zero.

Trivial!

]]>Math books, sine, recreational mathematics, etc.]]>