scalar product
- noun
- /ˈskeɪlər ˈprɒdʌkt/
- Specialized
:
producto escalar
- In linear algebra, the scalar product is often referred to as the dot product and yields a single real number.
Examples
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So you're essentially taking the scalar product here, Phi beta, Phi beta.
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The image of the imported scalar product, mapping pairs of those curves through a point of the globe to ???2, is the usual scalar product of the respective tangent vectors.
Academic text (1998) -
And if we square it on the right hand side, we have the scalar product of J&S.
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Then now we have to look at the scalar product CF of X and we have to show that this is bounded.
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So that's why it's often called the scalar product, because the dot product results in a number, and so you can think of a scalar as a number.
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The imported scalar product can now be seen, cum grano salis, as follows:
Academic text (1998) -
Mechanical power, the rate of change of energy due to mechanical sources, is the scalar product of force and velocity (F x v), or torque and angular velocity (T x w).
Academic text (1999) -
To see how a metric can be "imported" on the globe, one regards the usual Euclidean scalar product and remembers that the import of the usual Euclidean scalar product is achieved locally, for each point separately.
Academic text (1998) -
The scalar product of two vectors is calculated by multiplying their corresponding components and then adding the results together.
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To find the angle between two vectors, you can use the scalar product and the magnitudes of the vectors.
Synonyms
1
8.0
A number you get from two lists of numbers by multiplying and adding matching parts
A number made by multiplying pairs of numbers from two lists and adding them
Surface Forms
Morphology
The term is partly compositional: 'scalar' (a single number) combined with 'product' (result of multiplication) signals a product that yields a single number, which is a transparent clue. However, the precise mathematical operation (dot product of vectors, sum of componentwise products) is technical and not fully predictable to a B1 learner without domain knowledge, so it is only partially transparent.
Etymology
Scalar product comes from a simple image: you multiply two vectors and get one number. The word scalar points to that 'single number' result and product shows it comes from multiplying, so the name tells you what it does.