Explanation for "a vector in a linear space"?

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Hi,

my friend would like to know what this means: "a vector in a linear space". Someone mentioned about it in a video she some time ago saw, but he didn't explain it further because that video didn't relate to math. Could someone explain what it means? What are a vector and a linear space?

Google is your friend:

https://www.khanacademy.org/math/linear ... and_spaces

http://pirate.shu.edu/~wachsmut/Teachin ... spaces.pdf

Good luck!

Thank you! My friend has tried finding information on that online, but she hasn't understood anything about it, not even what they were explaining in that video. She's very bad at math. Could someone explain it better?

A vector can be expressed in two general ways: by angle and magnitude, and by orthogonal coordinates.

Linear space is a volume with regular increments that do not vary.

Thus, consider a cubic volume. It is a linear space. Now consider a line segment from one corner to the opposite corner. It is a vector. It has length (magnitude) and angular components. It can also be expressed in orthogonal components of X, Y, and Z.

{X0,Y0,Z0} to {X1,Y1,Z1}

I hope this helps!