Scalars

Scalars might best be introduced as simple numbers like 2 or 5 that can be used multiplied against any mathematical object.

In the math below, the 2 is a scalar:

2 * \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} = \begin{bmatrix} 2 \\ 4 \\ 6 \end{bmatrix}

You use the concept of a scalar when you double, triple, or halve a value.

More technically, for something to be a scalar, it must operate on a math object in a way that the answer is also that math object.

  • A vector multiplied by a scalar is a vector
  • A matrix multiplied by a scalar is a matrix