Please enable JavaScript.

Coggle requires JavaScript to display documents.

Linear algebra systematized (Vector (Definition (Geometric…

- - - - arrays of numbers
        
        notation
        
        row vector
        
        column vector
        
        2d vector: [x, y]
        
        3d vector: [x, y, z]
        
        4d vector: [x, y, z, w]
    - - directed line segment that has magnitude and direction
      - Characteristics
        
        vector do not have position, only magnitude and direction
        
        for example
        
        Displacement: “Take three steps forward.” This sentence seems to
        be all about positions, but the actual quantity used in the sentence is
        a relative displacement and does not have an absolute position. This
        relative displacement consists of a magnitude (3 steps) and a direction
        (forward), so it could be represented by a vector.
        
        Velocity: “I am traveling northeast at 50 mph.” This sentence de-
        scribes a quantity that has magnitude (50 mph) and direction (north-
        east), but no position. The concept of “northeast at 50 mph” can be
        represented by a vector.
        
        Can be used to represent relative displacement and velocity
        
        displacement and velocity are technically different from distance and speed which are scalar quantities
        
        distance is the magnitude of vector quantity displacement
        
        speed is the magnitude of vector quantity velocity
        
        Because vectors are used to express displacements and relative differ-
        ences between things, they can describe relative positions. (“My house is
        3 blocks east of here.”)
  - - - For example, in 2D, we list the displacement parallel to the x-axis, and the displacement parallel to the y-axis