LIFESCI 30A Lecture Notes - Lecture 8: Scalar Multiplication

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When drawing a vector field, draw the state space and a change vector going through a particular position. Vector fields require special attention to detail. Usually, abstractly, vectors do not need to be in a specific position. [4 1] + [-2 3] = [2 4] this new value becomes the next state. Starting state + change vector = later state. Learn to add vectors visually by attaching vectors. Scaling a vector means to use a scalar (factor) to multiply to a vector: Going over by 2 and up by 3. To draw a state vector as an arrow instead of as a point, always draw it starting at the origin. Then, the new state it represents is located at the tip of the arrow. Later state = starting state + change vector. This also means you can get a change vector as later state minus starting state. If [j r] = [5 0] then [j" r"] = [0 -5]

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