Adjectivedimensional (comparative more dimensional, superlative most dimensional) Positive dimensional Comparative more dimensional Superlative most dimensional
From Wiktionary under the GNU Free Documentation License. In mathematics and physics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify each point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it (for example, to locate a point on the surface of a sphere you need both its latitude and its longitude). The inside of a cube, a cylinder or a sphere is three-dimensional because three co-ordinates are needed to locate a point within these spaces. In physical terms, "dimension" refers to the constituent structure of all space (cf. volume) as well as the spatial constitution of objects within —structures that have correlations with both particle and field conceptions, interact according to relative properties of mass, and which are fundamentally mathematical in description. Physical theories that incorporate time, such as general relativity, are said to work in 4-dimensional "spacetime", (defined as a Minkowski space). Modern theories tend to be "higher-dimensional" including quantum field and string theories. The state-space of quantum mechanics is an infinite-dimensional function space. The concept of dimension is not restricted to physical objects. High-dimensional spaces occur in mathematics and the sciences for many reasons, frequently as configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in. From Wikipedia under the
GNU Free Documentation License How do I write a C program reads a 5x5 two-dimensional array of integers and prints the row and column sums? Q. How do I write a C program that reads a 5x5 two-dimensional array of integers and then prints its row sums and column sums? Asked by Lora - Sun Oct 25 13:06:34 2009 - - 4 Answers - 0 Comments A. And don't forget to use the debugger to single step through and makes sure the code is executing as intended! Answered by John T - Sun Oct 25 13:18:26 2009 If a line is composed of many 0-dimensional points, how can it have any length? Q. In other words, how can a collection of nothing make something? Note: I understand that physically, all points we see and draw are not 0-dimensional and so they in fact have size. So physically, a line is composed of many tiny spheres and the line in actuality is something like a cylinder. However, I am asking with regard to a line in the mathematical/conceptual sense. Asked by Ryan O - Thu Nov 27 11:07:38 2008 - - 4 Answers - 0 Comments A. There is a distinction between countably infinite and uncountably infinite. An uncountably infinite set of things with no dimension can add up to something with dimension. Peculiar things happen with infinity. You must not treat it like an ordinary number. Answered by mathsmanretired - Thu Nov 27 11:18:39 2008 How is a "Hilbert Space" different from a finite dimensional vector space?
Q. How is a Hilbert Space different from a finite dimensional vector space? I am familiar with using matrices to do linear transformations in Euclidean n-space, but how is this done in an infinite dimensional space? Are matrices still used? I have read definitions in books but I can't seem to make sense of them. How would you actually go about computing a transformation using these spaces? Asked by Runa - Fri Jan 26 18:54:31 2007 - - 2 Answers - 0 Comments A. With a finite dimensional (real) inner product space, you essentially identify the space with Euclidean space by choosing a basis. Namely, if V is the space and {v_1, ... , v_n} is a basis, then a linear transformation T:V -> V is represented by the matrix A whose columns are the coordinates of T(v_1), ... , T(v_n). You could try to do the same thing with an infinite dimensional Hilbert space. And this may be useful, but now when you multiply matrices, the issue of convergence arises: if A and B are infinite matrices, then to compute the entries of AB you need to sum infinite series. You ask about how this is different from the finite dimensional setting. Here's an interesting difference. If V is finite dimensional, and T admits a… [cont.] Answered by Dr. Mobius - Fri Jan 26 22:09:09 2007 From Yahoo Answer Search: "dimensional"  news.google.com VentureBeat With three- dimensional visual effects, the game becomes blurry, imprecise, and disorienting. It's still a work in progress, as Killzone 3 isn't coming out ... Next Killzone game to be in 3D Stuff Middle East (blog) all 84 news articles » news.google.com antiMUSIC.com Here it is again: Lightning Swords Of Death are set to release their second album, The Extra- Dimensional Wound, on May 25th. They've already completed tours ... an interview w/ Lightning Swords of Death & a new MP3 Brooklyn Vegan (blog) all 3 news articles » news.google.com Suncoast News Forbes had been one of the first in the area to install new technology that produces three- dimensional X-rays of teeth, at his Dunedin office. ... and more » From Google News Search: "dimensional"  images.inmagine.com 400px x 271px | 20.70kB [source page] Specification Keywords Login to view Non Watermarked image  fairgotrading.com.au 437px x 350px | 32.10kB [source page] This unique and fine detailed tri dimensional nativity is perfect for a unique addition to your tree Hand crafted the detail and From Yahoo Image Search: "dimensional"  en.aids1201.com banjia1 Sat, 12 Jun 2010 17:19:20 GM It is reported that the sea-. dimensional. Ti Ai (VTI) Biological Research Institute of vaccine technology from the United States in Haikou incorporated a high-end bio-technology research and development institutions; mainly of new ...  divisbyzero.com Dave Richeson Sun, 09 May 2010 17:30:45 GM As Wikipedia points out, 100 evenly-spaced sample points suffice to sample a unit interval with no more than 0.01 distance between points; an equivalent sampling of a 10-. dimensional. unit hypercube with a lattice with a spacing of 0.01 ...  earth-wikipedia.com earth-wikipedia Sat, 22 May 2010 07:00:00 GM May 24, 1953 three-. dimensional. film for the first time, in order to bring viewers back to television, Hollywood released a new items can three-. dimensional. movies. Viewers wearing special glasses to watch as bois devil and wax ... From Google Blog Search: "dimensional" |
