An endomorphism is a homomorphism from a mathematical structure to itself, preserving the structure's operations and relations. It is a fundamental concept in abstract algebra and linear algebra, providing insight into the internal symmetries and transformations of the structure.

Endomorphism

endomorphism

A homomorphism is a structure-preserving map between two algebraic structures, such as groups, rings, or vector spaces, that respects the operations defined on these structures. It is a fundamental concept in abstract algebra, allowing the transfer of properties and the study of structural similarities between different algebraic systems.

homomorphism

A mathematical structure is a set or sets equipped with additional features, such as operations or relations, that adhere to specific axioms or properties. These structures are foundational in mathematics, providing a framework for analyzing and solving problems across various fields such as algebra, geometry, and topology.

mathematical structure

Abstract algebra is a branch of mathematics that studies algebraic structures such as groups, rings, and fields, focusing on their properties and the relationships between them. It provides a unifying framework for understanding mathematical concepts and solving problems across various areas of mathematics and science.

abstract algebra

Linear algebra is a branch of mathematics that deals with vector spaces and linear mappings between these spaces, focusing on the study of lines, planes, and subspaces. It is fundamental in various scientific fields, providing tools for solving systems of linear equations, performing transformations, and analyzing vector spaces and matrices.

linear algebra

internal symmetries

Transformations refer to operations that alter the form, appearance, or structure of something, often used in mathematics and science to describe changes in position, shape, or size while preserving certain properties. They are fundamental in understanding symmetry, geometry, and the behavior of functions and systems across various domains.

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