Euclidean space This article is about Euclidean spaces of all dimensions. For 3-dimensional Euclidean space, see 3-dimensional space. A sphere, the most perfect spatial shape according to Pythagoreans, also is an important concept in modern understanding of Euclidean spaces Every point in three-dimensional Euclidean space is determined by three coordinates. Intuitive overview[edit] In order to make all of this mathematically precise, the theory must clearly define the notions of distance, angle, translation, and rotation for a mathematically described space. Once the Euclidean plane has been described in this language, it is actually a simple matter to extend its concept to arbitrary dimensions. Euclidean structure[edit] These are distances between points and the angles between lines or vectors, which satisfy certain conditions (see below), which makes a set of points a Euclidean space. where xi and yi are ith coordinates of vectors x and y respectively. Distance[edit] Angle[edit] (explain the notation),

How the Stock Market and Economy Really Work - Kel Kelly "A growing economy consists of prices falling, not rising." The stock market does not work the way most people think. A commonly held belief — on Main Street as well as on Wall Street — is that a stock-market boom is the reflection of a progressing economy: as the economy improves, companies make more money, and their stock value rises in accordance with the increase in their intrinsic value. A major assumption underlying this belief is that consumer confidence and consequent consumer spending are drivers of economic growth. A stock-market bust, on the other hand, is held to result from a drop in consumer and business confidence and spending — due to inflation, rising oil prices, high interest rates, etc., or for no reason at all — that leads to declining business profits and rising unemployment. The Fundamental Source of All Rising Prices For perspective, let's put stock prices aside for a moment and make sure first to understand how aggregate consumer prices rise. Forced Investing

Hilbert space The state of a vibrating string can be modeled as a point in a Hilbert space. The decomposition of a vibrating string into its vibrations in distinct overtones is given by the projection of the point onto the coordinate axes in the space. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as infinite-dimensional function spaces. The earliest Hilbert spaces were studied from this point of view in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer)—and ergodic theory, which forms the mathematical underpinning of thermodynamics. Definition and illustration[edit] Motivating example: Euclidean space[edit] The dot product satisfies the properties: Definition[edit] The inner product of an element with itself is positive definite: converges.

How a blind girl sees the world. (Animation) é€™æ˜¯ç”±å°ç£è—è¡“å¤§å¸ å¤šåª’é«”å‹•ç•«è—è¡“å¸ç³» 95ç´šçš„ä¸‰ä½ç•¢æ¥ç”Ÿæ‰€è£½ä½œçš„ç•¢æ¥çŸç‰‡æ•…äº‹æ˜¯æ•˜è¿°ä¸€ä½å°å¥³å©å› ç‚ºè¢«æ¶åŠ«è€Œé›¢é–‹åŽŸæœ¬ç†Ÿæ‚‰çš„é“è·¯ï¼Œåœ¨ç©¿éŽç±¬ç¬†å¾Œçš„æœªçŸ¥ä¸–ç•Œï¼Œé è‘—è¦–è¦ºä»¥å¤–çš„æ„Ÿå®˜å±•é–‹ä¸€å ´å¤§å†’éšªã€‚å…¨ç‰‡æŽ¡å–æ°´å½©ç¹ªè£½çš„èƒŒæ™¯èˆ‡æ‰‹ç¹ªå‹•ç•«æé…çš„è£½ä½œæ–¹å¼ï¼Œä»¥ç¹ªæœ¬å¼çš„ç”¨è‰²å’Œç°¡å–®çš„äººç‰©é€ åž‹å‘ˆç¾å°å¥³å©æƒ³åƒä¸çš„ä¸–ç•Œã€‚This is a graduation Production made by three students graduated from the National Taiwan University of Arts. The main character of little girl in the story confronts a robbery and strays from the road she is familiar with. After passing a hedge, she enters an unknown world and unfolds a magical adventure depending on senses other than vision and her imagination. Tags

Octave Executable versions of GNU Octave for GNU/Linux systems are provided by the individual distributions. Distributions known to package Octave include Debian, Ubuntu, Fedora, Gentoo, and openSUSE. These packages are created by volunteers. The delay between an Octave source release and the availability of a package for a particular GNU/Linux distribution varies. The Octave Wiki has instructions for installing Octave on macOS systems. Octave may also be available in third-party package managers such as Homebrew, MacPorts, or Fink. Executable versions of Octave for BSD systems are provided by the individual distributions. The latest released version of Octave is always available from

Ten games that make you think about life At the start of this year, we decided to come up with a list of Flash casual games with a philosophical bent. To be honest, we struggled. After days of research, we could only find a handful of games that had the thought-provoking depth we were looking for. Fast forward to now, and it is remarkable how much difference a few months can make. In a wonderful twist, it seems it is the Flash gaming space - until now known more for the throwaway nature of its games rather than depth - that is leading the way in this exciting new area of gaming, as we hope the following games prove. One you have finished playing these games, check out our follow-up lists: Ten More Games That Make You Think About Life and Another 20 Games That Make You Think About Life. 1Immortall The game starts with you crash landing on a planet. 2Loved Take a cursory look at Alexander Ocias's Loved, and you could mistake it for a pretty basic platformer. 3I Can Hold My Breath Forever 4The Company of Myself 5Coma 6Loondon

Big O notation Example of Big O notation: f(x) ∈ O(g(x)) as there exists c > 0 (e.g., c = 1) and x0 (e.g., x0 = 5) such that f(x) < cg(x) whenever x > x0. Big O notation characterizes functions according to their growth rates: different functions with the same growth rate may be represented using the same O notation. The letter O is used because the growth rate of a function is also referred to as order of the function. A description of a function in terms of big O notation usually only provides an upper bound on the growth rate of the function. Associated with big O notation are several related notations, using the symbols o, Ω, ω, and Θ, to describe other kinds of bounds on asymptotic growth rates. Big O notation is also used in many other fields to provide similar estimates. Formal definition[edit] Let f and g be two functions defined on some subset of the real numbers. if and only if there exist positive numbers δ and M such that if and only if Example[edit] For example, let so Usage[edit] or and . . . .

Interesting things, humor, facts, videos, wallpapers, plus funny and cool t shirts | I Like To Waste My Time Machine Learning Machine learning is the science of getting computers to act without being explicitly programmed. In the past decade, machine learning has given us self-driving cars, practical speech recognition, effective web search, and a vastly improved understanding of the human genome. Machine learning is so pervasive today that you probably use it dozens of times a day without knowing it. This course provides a broad introduction to machine learning, datamining, and statistical pattern recognition.

Video Lectures | Introduction to Computer Science and Programming | Electrical Engineering and Computer Science 12 IT skills that employers can't say no to Have you spoken with a high-tech recruiter or professor of computer science lately? According to observers across the country, the technology skills shortage that pundits were talking about a year ago is real (see "Workforce crisis: Preparing for the coming IT crunch"). "Everything I see in Silicon Valley is completely contrary to the assumption that programmers are a dying breed and being offshored," says Kevin Scott, senior engineering manager at Google Inc. and a founding member of the professions and education boards at the Association for Computing Machinery. "From big companies to start-ups, companies are hiring as aggressively as possible." Also check out our updated 8 Hottest Skills for '08. Many recruiters say there are more open positions than they can fill, and according to Kate Kaiser, associate professor of IT at Marquette University in Milwaukee, students are getting snapped up before they graduate. (See also "The top 10 dead (or dying) computer skills".) 1) Machine learning

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