Back Násobení skalárem Czech Skalarmultiplikation German Βαθμωτός πολλαπλασιασμός Greek Skalara multipliko Esperanto Multiplicación escalar Spanish ضرب نرده‌ای Persian Multiplication par un scalaire French כפל בסקלר HE Perkalian skalar ID 스칼라 곱셈 Korean

Scalar multiplication

Not to be confused with scalar product.
Scalar multiplication of a vector by a factor of 3 stretches the vector out.
The scalar multiplications −a and 2a of a vector a

In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra[1][2][3] (or more generally, a module in abstract algebra[4][5]). In common geometrical contexts, scalar multiplication of a real Euclidean vector by a positive real number multiplies the magnitude of the vector without changing its direction. Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and is to be distinguished from inner product of two vectors (where the product is a scalar).

  1. ^ Lay, David C. (2006). Linear Algebra and Its Applications (3rd ed.). Addison–Wesley. ISBN 0-321-28713-4.
  2. ^ Strang, Gilbert (2006). Linear Algebra and Its Applications (4th ed.). Brooks Cole. ISBN 0-03-010567-6.
  3. ^ Axler, Sheldon (2002). Linear Algebra Done Right (2nd ed.). Springer. ISBN 0-387-98258-2.
  4. ^ Dummit, David S.; Foote, Richard M. (2004). Abstract Algebra (3rd ed.). John Wiley & Sons. ISBN 0-471-43334-9.
  5. ^ Lang, Serge (2002). Algebra. Graduate Texts in Mathematics. Springer. ISBN 0-387-95385-X.

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