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