projektsioone

Projektsioone is an Estonian term that denotes projection in various technical and practical contexts. It is used to refer to both the act of projecting and the resulting image or mapping, and the plural form projektsioone emphasizes multiple instances or types of projection.

In mathematics, projektsioon refers to a projection operator: a linear transformation P on a vector space that satisfies P squared equals P (P^2 = P). Such an operator leaves every vector in its image unchanged and decomposes the space into the direct sum of the image and the kernel. A common special case is the orthogonal projection onto a subspace, where vectors are projected perpendicularly to that subspace.

In computer graphics and computer vision, projektsioon describes the process of mapping 3D coordinates to a 2D plane, such as a camera sensor or a viewport. Perspective projection uses a projection matrix to simulate depth and perspective, while orthographic projection preserves size and shapes along parallel lines, ignoring depth.

In film, theatre, and educational settings, projektsioon refers to displaying motion pictures or images on a screen using a projector. This sense emphasizes the practical act of presenting visual content to an audience.

In data analysis and statistics, projektsioon can denote projecting high-dimensional data onto a lower-dimensional subspace, a step common in dimensionality reduction techniques such as principal component analysis, where the goal is to retain as much variance as possible in fewer dimensions.

See also: projektsioon, projektor, projection, projection matrix, orthogonal projection, perspective projection.