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Vector Spaces

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GIve  a few examples of  functionals on the vector space \(R^3\)
of vectors in three dimensions. Later we will check which of these
are linear and which ones are not linear.

Following examples were given by the students in the class.

  1. \( \Psi_1(\vec{A}) = A_1+A_2+A_3 \)
  2. \(\Psi_2(\vec{A}) = A_1 A_2 + A_2A_3 + A_3A_1\)
 
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