Linear Algebra - Point

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Zero-dimensional: Span of the empty set: The origin

A point (x, y) can be represented in the plane by a {'x','y'}-vector<math>\begin{bmatrix} x \\ y \end{bmatrix}</math> .

A point can also be represented by {'x','y','z'}-vector<math>\begin{bmatrix} x \\ y \\ z\end{bmatrix}</math> . This representation is called homogeneous coordinates

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in Geometry An object can be: a pre-defined shape or an arbitrary one defined with the help of a path. Notions such as: The length of a vector The angle between two vectors. are introduced...
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Geometry - Origin

All geometrics objects definition goes through the origin. In order to go through an another point, a translation (addition) must be performed.
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Given a point b and a plane, find the point in the plane closest to b. By , we can assume the plane includes the origin. The plane is a vector space V. Let {v1, v2} be a basis for V. Goal: Given...
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coordinate system in terms of vector. Idea of coordinate system for a vector space V: (and generalized beyond two dimensions), Coordinate system for a vector space V is specified by generators of...
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A generalized image consists of a grid of generalized pixels, where each generalized pixel is a quadrilateral (not necessarily a rectangle). Think of an image as a grid of rectangles, each assigned a...
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Linear Algebra - Vector

tuple in Linear algebra are called vector. A vector is a list of scalar (real number) used to represent a When the letters are in bold in a formula, it signifies that they're vectors, To represent...

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