Recent content by rkaminski

Dear All, I think I understand the idea, and the flow of the reasoning. Especially what Hawkeye18 wrote. We first define the space with the selected inner product, on that basis we define the norm, the orthonormal basis ets. Now my question would be why exactly in "real" Euclidean space (our...

Your answer explains that we can obtain an inner product from the norm. The attached PDF file gives more details. To me, it seems like just swapping the problem around. The question is rather why we define the inner product (or the norm) like I wrote, in the case of Euclidean spaces? What would...

Dear All, Here is one of my doubts I encountered after studying many linear algebra books and texts. The Euclidean space is defined by introducing the so-called "standard" dot (or inner product) product in the form: (\boldsymbol{a},\boldsymbol{b}) = \sum \limits_{i} a_i b_i With that one...

But is my original 'definition' of the canonical basis wrong or incomplete? Is this definition even needed at all? Because still, my understanding is that all possible set of basis vectors for a given vector space (for simplicity in 2D) can be expressed as (1,0) and (0,1).

OK. So there is my problem, maybe it arises from my bad understanding of the definition. According to the above example, consider a Cartesian coordinate system. It obviously has two basis vectors: (1,0) and (0,1), and this set of vectors fulfills this a 'definition' of the canonical basis. Now...

In many places the canonical basis is defined as a set of vectors with coordinates as: \boldsymbol{e}_i=(0,...,1,...0) where "1" is on the i-th place. In my undestanding of such definicion every basis is canonical basis. If we write coordinates of basis vectors in the same basis we will get such...

And does any author discuss these issues at the elementary level, not pointing out to the formalism of differential forms?

OK. A problem is simple and probably very stupid... In many (most of) maths books things like Euclidean metric, norm, scalar product etc. are defined in Cartesian coordinate system (that is one which is orthonormal). But what would happen if one were to define all these quantities in...

Hi JJacquelin, I will have a look at the French papers you send. These are very interesting. No problem for me to understand them:) However, I don't understand your last post. Non-linear least-squares method does require initial values of the parameters. That is why the procedure needs to...

Dear All, I would like to do an exponential function least-squares fitting, but having two or more exponents. For example the function looks like this: y (x) = A \exp (-x/a) + B \exp (-x/b) where A, a, B and b are the least-squares fitted parameters. My question is how to obtain the...