# dimensional

1. ### Invertible Dimensional Matrices

Suppose A, B, and C are invertible 4x4 dimensional matrices with the properties that det(A)=3, det(B)=5, and det(C)=2. Calculate the determinant of: (3A^(-1)BCC^(T)A^(3)) I understand matrices and determinants but I can't figure out how to start this question...Could someone help? Once I know...
2. ### dimensional analysis?

In order to determine whether or not the patient had a mutation in exon 19 of the EGFR gene, the laboratory technologist had to set up PCR. She first extracted DNA from the tumor sample and then quantitated it. Her protocol stated that she needed to add 25ng to her 50uL reaction. After...
3. ### Dimensional Analysis

Not sure if this is the right section? Im really struggling with this - it is found experimentally that the terminal velocity (ut) of a spherical particle in a fluid depends upon the diameter (d) of particle, the dynamic viscosity (u) of the fluid and the buoyancy weight (W) of the particle...
4. ### 2 dimensional integral

Can some one give me an example of a 2 dimensional integral over a region Q, such that one of the iterated integrals exist, but the other does not. I have tried sort of taking examples of functions that are not continuous, but the ones I have set up, just don't fit into the description. I...
5. ### Nonlinear, infinite dimensional ODE

Hi! In my derivations I have stumbled upon an ODE on the form \frac{d F_n}{dt} = a_n F_n(t)\left(\sum_{m = 1}^{\infty} b_m[F_m(t) - F_m(0)] - C\right) (no Einstein summation implied). F_n(t) are real valued, and a_n, b_n and C are constants. Does there exist an analytic solution to this...
6. ### 1 dimensional Geometry and Euclid proposition 4 and 8 in book I

I was reading Euclids book and it is really good. He starts with plane geometry and then he does solid geometry and after that I want to read some other peoples books about hyperspace geometry but plane geometry is 2 dimensional so that means he skipped 1 dimensional geometry. Is there a...
7. ### not finite dimensional

Prove that the vector space P of all polnomials is not finite dimensional??
8. ### Solving higher dimensional systems of inequalities

Solving a 2-dimensional system of inequalities is simple enough, but it occurred to me the other day that I don't really know how to go about solving higher dimensional systems. The problem I was tinkering around with was to find (preferably integer) numbers, a, b, c, d, x, y and z, such that...
9. ### Infinite Dimensional Vector Space

Dear Members Kindly guide me about Infinite Dimensional Vector Space? I am requested to give easy examples Infinite Dimensional Vector Space with proof. Waiting for good response.
10. ### Popular high dimensional geometry

Recently, I was watching a book called "popular high dimensional geometry", feel good and to share with everyone, everyone if there are other books of higher algebra, share the happiness together! If you have any questions please contact [email protected] Thank you
11. ### Dimensional Analysis

I would like non-dimensionalize the equations which describe a non-Newtonian fluid model. In the constitutive equation (power-law model) there is a non-dimensional parameter: n. According to Buckingham's Pi theory, I must take all the relevant independent parameters (variables, constants, etc.)...
12. ### 4 dimensional cube properties

lets construct a 4D cube, it has 2^4=16 corners and 2*4=8 3D faces and 24 2 dimensional faces. the 8 3D faces contribute 4 edges and the total edges is 8*4=32. so can you know these properties by deduction or visualization somehow? maybe there is an Euler characteristic? anyway I guess...
13. ### Fitting a Gaussian to high dimensional data with a discrete pdf defined over them

Hi, I wonder if anyone can give me a handle on this problem. I have sampled 100,000 point from an isometric gaussian in 98 dimensional space (each point translates into a particular face in a "face space" model). I have then defined a uniform distribution over the 100, 000 points. so far so...
14. ### dimensional analysis for metric conversions

I need to learn how to solve metric conversions through dimensional analysis. Can someone please help any info would be greatly appreciated.
15. ### Distance between a point and closed set in finite dimensional space-functional analys

Let X be a linear normed space. I need to prove that X is finite dimensional normed space if and only if for every non empty closed set C contained in X and for every x in X the distance d(x,C) is achieved in specific c. I know how to prove the direction which assumes X is finite dimensional...
16. ### Help on 2 dimensional Markov chains

Hello, my name is Koustubh. I have a question regarding two dimensional Markov chain. Lets say that there are three states viz. 1,2,3 and in the spatial domain there are 3 regions say A,B,C. Now I have Tranisition probability Matrices for states and region separtely. Transition can occur...
17. ### Infinite Dimensional Cross Product

It has been proved that cross product of vectors just is satisfied in 3D space and also in 7D and 8D spaces as specific cases. Besides, there are some other multiplication schemes of vectors such as wedge product, Ersatz cross product ... that are not quite the cross product (they do not satisfy...
18. ### Definite Integrals in Infinite Dimensional Space

As it can be easily found in literature, indefinite integrals are treated as inner product of infinite dimensional vectors. But what about definite integrals? When we deal with definite integrals, I think, we would have been previously defined the associated vectors such that the integration...
19. ### (n - 1) dimensional submanifold of the manifold R^n

Let A be a symmetric n \times n matrix over \mathbb{R}. Let 0 \neq b \in \mathbb{R}. Show that the surface M = \{x\in \mathbb{R}^n \mid x^T A x = b\} is an (n - 1) dimensional submanifold of the manifold \mathbb{R}^n. Please, help!
20. ### Need help with the optimization of volume of 3 dimensional shapes.

A right circular cylinder is inscribed in a cone with height H and base radius R. Find the largest volume of such a cylinder (you should assume they are rotated about the same axis). If you could please solve in a step by step manner and explain each step, I would greatly appreciate it. Thank you.