scalar matrix
- noun
- /ˈskeɪlər ˈmeɪtrɪks/
- Specialized
:
matriz escalar
- A scalar matrix is a square matrix where all the diagonal entries, such as 5's in a 3x3 matrix, are equal and the other entries are zero.
Examples
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To solve the problem, we first need to represent the transformation using a scalar matrix that multiplies each vector by a constant.
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They use templates to avoid creating intermediate objects for transposes or scalar-matrix products, just like a good Fortran compiler.
Blog text (32) -
In linear algebra, the simplest example of a scalar matrix is the matrix that has the same number repeated on the diagonal and zeros elsewhere.
Surface Forms
Morphology
The compound signals a matrix defined by a single scalar (’scalar’ = one number, ’matrix’ = array), so learners can infer that the matrix is determined by one number. However, the precise technical constraint (equal diagonal entries and zeros elsewhere, i.e. scalar times the identity) is specialized mathematical knowledge and not fully predictable from the constituents alone, making the term only partially transparent.
Etymology
The term scalar matrix comes from the idea that it is a matrix made by multiplying the identity by one scalar, a single number. Because every diagonal entry is the same, the scalar matrix simply scales every vector by that number, so it behaves like multiplying by that scalar.
