State Space: Rules for Operating with Vectors

Summary

• “Vector Space” has two rules for operating on vectors
• first rule: vector addition

  In \(1\) variable, we have, say \(X_1\) and \(X_2\), two numbers. We know how to add two numbers, so we can make a new \(1\)-vector "\(X_1 + X_2\)" in the same space

• second rule: scalar multiplication.

  multiplication of a \(1\)-vector by a number. (called a “scalar”)

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• units in state spaces

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• 2-vectors

  how to add \( (S_1, T_1) \) to \( (S_2, T_2) \) to get \( (S_3, T_3) \)

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• geometry
  • adding two \(1\)-vectors geometrically in state space
  • multiplying a \(1\)-vector by a scalar