Vector as a collection of numbers


Draw a number line and place the number 0, or the origin, in the middle. To the right is the positive direction, and to the left is negative. A position on this line can be represented by a single real number.


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Draw another number line vertically, orthogonal to the first one. Either direction is fine, but let's assume that the top is positive and the bottom is negative. With two real numbers, a point on a plane can be represented.


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By adding another line perpendicular to the first two number lines, we can now represent a point in three dimensions using three real numbers.


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A vector is a tuple of several numbers put together like these, and each number in a vector is called a component.


Vector is defined differently depending on the field, especially in mathematics, where we sometimes consider a more abstract vector space.


Vectors don’t always have to represent positions in space. For example, the RGB or HSB values of a color can also be thought of as a three-dimensional vector. Conversely, any data consisting of multiple numbers can be mapped to a space, or we can think of some kind of space they live. Colors mapped to a space is called a color space, and we can think about the distance or orientation between colors.