Linear Algebra nature - what exactly is a vector?

First, think of three viewpoints vector

Expression vector in physics, mathematics, computer

• From a physical Professional perspective: arrow vector space is determined a vector is its length and direction and it refers. As long as the same length and direction, you can move freely and a vector it remains unchanged.
• From a computer professional perspective: vector is an ordered list of arrays.
• From a mathematical professional perspective: roughly speaking, the vector can be anything, as long as the two vectors and vector adding and multiplying numbers makes sense to.

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• In the two-dimensional plane: coordinates of a vector consists of a pair of numbers, which is a few instructions on how you start from the origin (the starting point of the vector) to reach its tip (vector end).
• In the three-dimensional space: each vector corresponding to an ordered triple.

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Second, the vector and

• In the two-dimensional plane: V, Wtwo vectors are added, the Wvector translation, so that its start and Vend points of the vector coincide, then draw a vector, that from the Vstart of the starting point of the vector, pointing Wthe end of the vector. The painted vector, and is their.
  
  

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Third, the vector multiplication

• Multiplied by a negative vector, the vector is inverted.
• Multiplying the vector number, called a scalar .
• Vector and scalar multiplication, each component is multiplied by the scalar and vector.

Reproduced in: https: //www.jianshu.com/p/d59f8bf3a25e