an operation used in the definition of a vector space in which the product of a scalar and a vector is a vector. The operation is distributive over the addition of both scalars and vectors, and is associative with multiplication of scalars
Examples of 'scalar multiplication' in a sentence
scalar multiplication
This new structure comprises a semigroup structure, a scalar multiplication and a compatible partial order.
Priti Sharma, Sandip Jana 2018, 'An algebraic ordered extension of vector space', Transactions of A. Razmadze Mathematical Institutehttp://www.sciencedirect.com/science/article/pii/S2346809217301423. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Compositions form a vector space in which addition and scalar multiplication are replaced by operations known as perturbation and powering.
Fiona Chong, Matthew Spencer 2018, 'Analysis of relative abundances with zeros on environmental gradients: a multinomialregression model', PeerJhttps://peerj.com/articles/5643.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Our 16-bit and 32-bit implementation results set new speed records for variable-base scalar multiplication.
Jihoon Kwon, Seog Chung Seo, Seokhie Hong 2018, 'Efficient Implementations of Four-Dimensional GLV-GLS Scalar Multiplication on 8-Bit,16-Bit, and 32-Bit Microcontrollers', Applied Scienceshttp://www.mdpi.com/2076-3417/8/6/900. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The allowed matrix operations are: matrix-by-matrix addition, subtraction, dot product and multiplication, matrix-by-vector multiplication, and matrix by scalarmultiplication.
Asgar Abbaszadeh, Taras Iakymchuk, Manuel Bataller-Mompeán, Jose V. Francés-Villora,Alfredo Rosado-Muñoz 2019, 'AnScalable Matrix Computing Unit Architecture for FPGA,and SCUMO User Design Interface',Electronicshttp://www.mdpi.com/2079-9292/8/1/94. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)