linear transformation
[ˈlɪniər trænsˌfɔrˈmeɪʃən]
nounpl: linear transformations
transformação linear
1. A function between two vector spaces that preserves the operations of vector addition and scalar multiplication
A linear transformation maps vectors from one space to another while maintaining linearity properties.
Uma transformação linear mapeia vetores de um espaço para outro, mantendo as propriedades de linearidade.
2. In mathematics, a map T: V → W between vector spaces such that T(av + bw) = aT(v) + bT(w) for all vectors v, w and scalars a, b
The transformation T(x, y) = (2x, 3y) is a linear transformation on R².
A transformação T(x, y) = (2x, 3y) é uma transformação linear em R².
3. A mathematical operation that can be represented by matrix multiplication
Every linear transformation can be represented as a matrix in a chosen basis.
Toda transformação linear pode ser representada como uma matriz em uma base escolhida.
Linear transformation is a fundamental concept in linear algebra taught universally in mathematics curricula across Brazil, Portugal, and the USA. The term is consistently translated as 'transformação linear' in both Brazilian and European Portuguese academic settings. It is essential terminology in engineering, physics, computer science, and advanced mathematics programs.
Related Idioms & Phrases
linear transformation between vector spaces
invertible linear transformation
singular linear transformation
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