| "Position-Quantity-Number" | "Point-Vector-Scalar"
|
| Number | Scalar
|
| Quantity (as a category such as "length", "weight", etc.) | Vector space (linear space)
|
| Quantity (as an element) | Vector
|
| Position (as a category such as "Height", "Time", etc.) | Space (of coordinates)
|
| Position(as an element) | Point
|
| Unit | Unit vector
|
| Origin | Origin
|
| Measure of a quantity | Expression of a vector in the form of linear combination of unit vectors
|
| Uniqueness of measure value (--> 1-dimensional) | Uniqueness of linear expression (--> 2-dimensional)
|
| Obtaining position | Obtaining coordinates
|
| Measuring scale | Axes of coordinates
|
| Sum of quantities | Sum of vectors
|
| Multiplying a quantity (Action of a number to a quantity) | Multiplying a vector (Action of a scalar to a vector)
|
| Proportional relation between two quantities | Linear function between two vector spaces
|
| Proportional function | Linear Transformation
|
| Constant of proportion | Matrix
|
From "Number and Quantity" to Linear Algebra