Linearity

• What is Linearity?
  • It refers to the conditions ① $F(v_1+v_2)=F(v_1)+F(v_2)$ and ② $F(\lambda v)=\lambda F(v)$ being satisfied.
  • I see, I kind of understand the gist.
  • So, in terms of scalar functions, it would only hold for something like $f(x)=kx”? (blu3mo)
  • This is about using it in operations.
• In physics, this corresponds to the Principle of Superposition (takker)
  • It’s interesting that there is a corresponding concept in physics, isn’t it? (blu3mo)(blu3mo)(blu3mo)(blu3mo)
  • Wave interference and electrical circuits are famous examples (takker)
    • Principle of Superposition - Wikipedia
    • What’s interesting is that some cases only approximate it.
      • For waves, it doesn’t hold when the amplitude becomes too large and intense.
      • It’s a typical example in physics where the dominant phenomenon changes when the scale changes.
        • Other examples include relativistic effects and quantum effects.