Vector Addition in Linear Algebra: ||x+y||2 = ||x||2 + 2*x*y + ||y||2

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SUMMARY

The discussion centers on the vector addition formula in linear algebra, specifically the equation ||x+y||² = ||x||² + 2*x·y + ||y||². Participants clarify that this equation represents the squared magnitude of the sum of two vectors x and y, derived from the dot product expansion (||x+y||² = (x+y)·(x+y)). The conversation emphasizes the importance of understanding the derivation and application of this formula in vector analysis.

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  • Familiarity with the concept of vector magnitude and its mathematical representation.
  • Basic knowledge of linear algebra principles and notation.
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||x+y||2 = ||x||2 + 2*x*y + ||y||2
 
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||x+y||^2=(x+y).(x+y) (dot product). Expand it out.
 
Is there a question here? Are you trying to prove that relation for two vectors x and y?

If so, what have you tried?
 

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