Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Linear Spaces Essay

A familiar example of a linear space is our everyday 3-dimensional Cartesian space of position vectors. In class, we've discussed several examples of linear spaces where the "vectors" are functions and not strictly magnitudes-and-direction vectors like , etc.   Give an example of a function vector space and compare and contrast it to Cartesian space.   Include in your discussion the concepts of basis vector, orthonormality, and completeness.   Note:   This is an essay question.  Your answer will be judged not solely on its correctness, but for its depth, coherence, and clarity.


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Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
Phone: (301) 405-6120

Last revision 2. December, 2005.