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"linear combination of" vs "linear combinations of"

Both phrases are correct, but they are used in different contexts. 'Linear combinations of' is used when referring to multiple linear combinations, while 'linear combination of' is used when referring to a single linear combination.

Last Updated: March 25, 2024

linear combination of

This phrase is correct and commonly used when referring to a single linear combination.

This phrase is used when discussing a single linear expression or vector that is a combination of other elements.

Examples:

  • The vector is a linear combination of the basis vectors.
  • Each data point can be seen as a linear combination of the features.

Alternatives:

  • combination of linear
  • mixture of linear
  • sum of linear
  • composition of linear
  • amalgamation of linear

linear combinations of

This phrase is correct and commonly used when referring to multiple linear combinations.

This phrase is used when discussing the combination of multiple linear expressions or vectors.

Examples:

  • The solution can be expressed as linear combinations of the given vectors.
  • We can represent the data as linear combinations of the basis vectors.

Alternatives:

  • combinations of linear
  • linear mixtures of
  • linear sums of
  • linear compositions of
  • linear amalgamations of

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