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linear combination

linear combination
Noun
pl: linear combinations

This term is a technical cornerstone of linear algebra, describing the process of scaling vectors and summing them to reach a new point in space. It carries a neutral, precise mathematical connotation and is used exclusively in academic, scientific, or engineering registers.

In practical application, the term implies a specific structural relationship where the components are linked by addition and scalar multiplication. It is distinct from a general "mixture" or "sum" because it requires the coefficients to be constants, maintaining the linearity of the operation.

Meanings

Nounlinear combination

An expression constructed from a set of terms by multiplying each term by a constant coefficient and adding the results together.

The resulting vector is a linear combination of the basis vectors.

Related Words

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