nomadreid's latest activity

Thanks for the replies, Gavran and Wrobel. First, Gavran. That is good to hear. Could you give me an example of each, and why? (That...

On the other hand consider a real Hilbert space ##F## of sequences ##x=(x_1,x_2,\ldots)## with inner product $$(x,y)_F=\sum_{k=1}^\infty...

Hope you are speaking about Hilbert spaces. If it is so you should separate two cases: a Hilbert space over ##\mathbb{R}## and over...

There is a difference. The difference lies not only in the fact that an inner product is bilinear and a dual space operation is linear...

Thanks for answering, Hill, although it appears that either I did not state the question clearly enough, or you read the question...

Starting with a vector space V equipped with an inner product (. , .), and its dual space V*, one can look at the expression <a|b> in...

Thanks very much, Gavron! I see my error now. I had not rid myself of my prejudice that isomorphism preserved all structures; I...

The transposition of a complex number is the same complex number, and the conjugation of a real matrix is the same real matrix. It is...

Thanks, Gavran, but apparently I did not express myself very well. Let me try again. First, if I understand your post correctly (but...

The conjugation of a complex number is also a complex number. So the conjugation of a complex number twice corresponds to the...

So, for example, if we take the Hermitian adjoint (the composition of the complex conjugate and the transpose), I would deduce from your...

Thanks, Gavron. These simple examples are very nice.

There is an isomorphism between the field of complex numbers and a specific set of 2x2 real matrices where a complex number ## a+bi ##...

Again, thanks, martinbn. Indeed. I think you mean I oversimplified or neglected the structures that accompany each.

But the usual identification of the complex numbers and the real plane sends ##a+bi## to ##(a,b)##. You are looking at something different.