Linear Algebra, unique minimizer of a quadratic function

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SUMMARY

The discussion focuses on the equality of the expressions xtKx* and x*^tKx* in the context of linear algebra, specifically within the framework of quadratic functions. The user seeks clarification on why these two expressions are equivalent, referencing the symmetry of inner products. The resolution involves multiplying out the left-hand expression of the second line of equation 4.13 to demonstrate the equality definitively.

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  • Familiarity with quadratic functions and their properties
  • Knowledge of matrix notation and operations
  • Basic concepts of symmetry in mathematical expressions
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  • Learn about quadratic forms and their applications
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Students studying linear algebra, mathematicians exploring quadratic functions, and educators teaching concepts related to inner products and matrix operations.

kristo
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Homework Statement


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The part I'm having problems with is where the last two expressions in 4.13 are equated. Why is xtKx*equal to x*^tKx*?

The Attempt at a Solution


xtKx* is an inner product and due to symmetry is equal to x*^tKx, but wouldn't equating x to x* mean every <x,y> = <x,x> = <y,y>?

Many thanks if someone decides to help me out.
 
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kristo said:
Why is xtKx*equal to x*^tKx*?
That's not what happened. Try multiplying out the left hand expression of the second line of 4.13.
 

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