Link: http://en.wikipedia.org/wiki/Newtonian_mechanics
Lagrangian Mechanics:
Link: http://en.wikipedia.org/wiki/Lagrangian_mechanics
Hamiltonian Mechanics:
Link: http://en.wikipedia.org/wiki/Hamiltonian_mechanics
Quantum Mechanics:
Link: http://en.wikipedia.org/wiki/Quantum_mechanics
Demension
Link: http://en.wikipedia.org/wiki/Dimension
Description:
In physics and mathematics, the dimension of a space is roughly defined as the minimum number of coordinates needed to specify every point within it[1][2]. For example: a point on the unit circle in the plane can be specified by two Cartesian coordinates but one can make do with a single coordinate (the polar coordinate angle), so the circle is 1-dimensional even though it exists in the 2-dimensional plane. This intrinsic notion of dimension is one of the chief ways in which the mathematical notion of dimension differs from its common usages.
Space:
Link: http://en.wikipedia.org/wiki/Space
Description:
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction.[1] Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime. In mathematics spaces with different numbers of dimensions and with different underlying structures can be examined. The concept of space is considered to be of fundamental importance to an understanding of the universe although disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.
Many of the philosophical questions arose in the 17th century, during the early development of classical mechanics. In Isaac Newton's view, space was absolute - in the sense that it existed permanently and independently of whether there were any matter in the space.[2] Other natural philosophers, notably Gottfried Leibniz, thought instead that space was a collection of relations between objects, given by their distance and direction from one another. In the 18th century, Immanuel Kant described space and time as elements of a systematic framework which humans use to structure their experience.
In the 19th and 20th centuries mathematicians began to examine non-Euclidean geometries, in which space can be said to be curved, rather than flat. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space.[3] Experimental tests of general relativity have confirmed that non-Euclidean space provides a better model for explaining the existing laws of mechanics and optics.
Hilbert spaces:
Link: http://en.wikipedia.org/wiki/Hilbert_space
Description:
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra from the two-dimensional plane and three-dimensional space to infinite-dimensional spaces. In more formal terms, a Hilbert space is an inner product space — an abstract vector space in which distances and angles can be measured — which is "complete", meaning that if a sequence of vectors is Cauchy, then it converges to some limit in the space.
Euclidean space:
Link: http://en.wikipedia.org/wiki/Euclidean_space
Description:Around 300 BC, the Greek mathematician Euclid undertook a study of relationships among distances and angles, first in a plane (an idealized flat surface) and then in space. An example of such a relationship is that the sum of the angles in a triangle is always 180 degrees. Today these relationships are known as two- and three-dimensional Euclidean geometry. In modern mathematical language, distance and angle can be generalized easily to 4-dimensional, 5-dimensional, and even higher-dimensional spaces. An n-dimensional space with notions of distance and angle that obey the Euclidean relationships is called an n-dimensional Euclidean space.
Eigenvalue, Eigenvector, Eigenspace:
Link: http://en.wikipedia.org/wiki/Eigenvalue
Description:
In mathematics, given a linear transformation, an eigenvector (help·info) of that linear transformation is a nonzero vector which, when that transformation is applied to it, may change in length, but it remains along the same line [the direction will "flip" if the eigenvalue is negative].
For each eigenvector of a linear transformation, there is a corresponding scalar value called an eigenvalue for that vector, which determines the amount the eigenvector is scaled under the linear transformation. For example, an eigenvalue of +2 means that the eigenvector is doubled in length and points in the same direction. An eigenvalue of +1 means that the eigenvector is unchanged, while an eigenvalue of −1 means that the eigenvector is reversed in sense. An eigenspace of a given transformation for a particular eigenvalue is the set (linear span) of the eigenvectors associated to this eigenvalue, together with the zero vector (which has no direction).