# gramschmidt

1. ### LinearAlgebra- Gram-Schmidt Algorithm and linear combinations

Hey guys, I have a problem relating to the Gram-Schmidt algorithm and expressing a vector as a linear combination of other vectors. Here is my attempt at doing the question. A B So I would like to know if I have done this correctly, and if not, how do I go about solving this question? Help...
2. ### Use Gram-Schmidt process to find an orthogonal basis for the image space A. QR Factor

Question is attached. I just would like someone to verify whether the answer involves fractions/mixed numbers because I do tend to get antsy when I see them in my work. I wonder if I did it right. So anyway here is what I got with Gram-Schmidt Process: With x1, x2, and x3 representing the...
3. ### Gram-Schmidt Process Calculation

Let P3 be the four-dimensional vector space of all polynomials of degree ≤ 3 with inner product <f,g> = integral of f(x)g(x).dx from -1 to 1. Apply Gram-Schmidt Process to basis {1, x, x2, x3} of P3 to obtain an orthonormal basis {z1, z2, z3, z4} for this inner product on P3. I got the...
4. ### gram-schmidt process help

Hi everyone, i need your help with solving the (ii) choice of the quesiton i attached,thanks for your helps .
5. ### Gram-Schmidt Problem

Hey, I was wondering if any of you could look at this problem for me, to be specific, problem 2c...
6. ### Gram-Schmidt process to find last row of matrix

Hi guys, Use the Gram-Schmidt process to find last row of the following orthogonal matrix where the first two rows are: [sqrt(3)/2, -1/sqrt(8), 1/sqrt(8)] and [0, 1/sqrt(3), sqrt(2)/sqrt(3)] (third row is [a,b,c]). Now, because the matrix is orthogonal, all of the rows are perpendicular...
7. ### I don't understand the Gram-Schmidt process on a function

I have been given a weight function w = xe^{-x} and u_n = x^n, n = 0,1,2,.. . I don't exactly get what bit to use to integrate because in my definition it says: \displaystyle \varphi_i = \frac{\psi_i}{\left(\int \psi_{i}^{2}wdx\right)^{1/2}} where \psi_i = u_i + a_{i,0}\varphi_0 +...
8. ### Gram-Schmidt process Help

Hey guys, I have a couple of questions that i need answered :( I have an exam coming up in a week and my prof. told me to answer a couple questions. I've worked out most of them but these three questions are really troubling me, if anyone can answer them and show me the steps I'd really...
9. ### Gram-Schmidt procedure

I need some help in applying the Gram-Schmidt procedure to the basis {v1; v2; v3} of R^3 ,where where v1 = (1; 1; 1) ; v2 = (0; 1; 1) ; v3 = (0; 0; 1);,in order to obtain an orthogonal basis of R^3 containing (1; 1; 1) and an orthonormal basis of R^3 containing (\frac{1}{\sqrt{3}}...
10. ### Gram-Schmidt

Hi, I learned Gram-Schmidt a few years ago, and now that I'm reading about it from another source I've having some problems with it. Suppose that O_k=\{u_1,u_2,\dots,u_k\} is an orthonormal basis for S_k=span\{x_1,x_2,\dots,x_k\}, and consider the problem of finding one additional vector...
11. ### Gram-Schmidt Process on these Vectors

I have a vector space of polynomials at most second degree with basis (1,x,x^2) with the inner product defined as \langle{p,q}\rangle=\int^{10}_{0}p(x)q(x)dx and I want to find an orthonormal basis using the Gram-Schmidt process. I've found that e_1=1/10 For e_2 I have...
12. ### Gram-Schmidt Proof

I'm stuck on this one part for the proof of the Gram-Schmidt which states if (v_1,\dots,v_m_) is a linearly independent list (my text uses the term list, but I believe the term set is used more often) of vectors in V, then there exist an orthonormal list (e_1,\dots,e_m) of vectors in V such that...
13. ### gram-schmidt procedure

I could use some help with the following... On P_{2}(R), consider the inner product given by <p,q>=\int_0^1 p(x)q(x) dx. Apply the Gram-Schmidt procedure to the basis (1,x,x^2) to produce an orthonormal basis of P_{2}(R).
14. ### Gram-Schmidt Question

If ql and q2 are the outputs from Gram-Schmidt, what were the possible input vectors a and b?
15. ### linear algebra Gram-Schmidt in Function Spaces problem

I attached the problem in the attachments, its easier to read this way. I know it seems long but the problems themselves aren't too long. We never really went over this stuff so I'm lost. If someone could guide me through these step by step that would really help for when I have my exam. Thank...
16. ### [SOLVED] Gram-Schmidt

the vectors {a1, a2, a3} are orthonormal the vector a4 is a combination x1a1 + x2a2 + x3a3 after applying gram schmidt to the set of vectors {a1, a2, a3, a4} the resulting set of vectors will be: {a1, a2, a3, zero vector} is this correct?
17. ### Gram-Schmidt method

do you integrate between 1 and 0 all the time. Or is it what c is the space of the continous function. As it is -1 and 1?
18. ### Gram-Schmidt Process

Im trying to understand the Gram-Schmidt process but i cant see how the part in this attatchment works? Could you please describe what's going on here? Thanks for any help in advance
19. ### Gram-Schmidt process question

Can anyone help me with this? I have to: apply the Gram-Schmidt process to the given subset S of the inner product space V to obtain an orthogonal basis for span(S), normalize it to obtain an orthonormal basis for span(S), and compute the Fourier coefficients of the given vector relative to the...
20. ### Gram-Schmidt Process

Let H be a seperable Hilbert space and M a countable dense subset of H. Show that H contains a total orthonormal sequence which can be obtained from M by the Gram-Schmidt process. (Itwasntme)