BIRKHOFF ORTHOGONALITY AND ANGLE CHARACTERISATION IN `1 N
There are various concepts regarding orthogonality in normed spaces, one of which is stated by mathematician G.D. Birkhoff (1884-1944). Birkhoff defined an orthogonality, in which the norm of a vector generated by adding a particular vector of reference with an arbitrary multiple of another vecto...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/47845 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | There are various concepts regarding orthogonality in normed spaces, one of which
is stated by mathematician G.D. Birkhoff (1884-1944). Birkhoff defined an orthogonality,
in which the norm of a vector generated by adding a particular vector of
reference with an arbitrary multiple of another vector should be greater or equal
than the norm of the vector of reference itself. This Final Project will discuss a
characterisation of acute and obtuse angles that is suitable with the definition of
Birkhoff orthogonality in a normed space. In particular, Birkhoff orthogonality and
angle in `1
n-space will be discussed. In addition, resolvability property of Birkhoff
orthogonality in `1
n will be also discussed; with focus on finding all possible values
of a which make the resolvability property holds for two arbitrary vectors in `1
n. |
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