(See Solution) Norm identities. Verify that the following identities hold for any two vectors a and b of the same size. (a+b)^T(a-b)=\|a\|^2-\|b\|^2. \|a+b\|^2+\|a-b\|^2=2(\|a\|^2+\|b\|^2)


Question: Norm identities. Verify that the following identities hold for any two vectors a and b of the same size.

  1. \((a+b)^{T}(a-b)=\|a\|^{2}-\|b\|^{2}\).
  2. \(\|a+b\|^{2}+\|a-b\|^{2}=2\left(\|a\|^{2}+\|b\|^{2}\right) .\) This is called the parallelogram law.

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