- ...rotation
- which of course actually lives in three-dimensional space but let's not
get carried away...
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- ...scalars)
- actually, what is going on here? The vector space
26#8 is defined over isn't a field, so can we really call its elements scalars? If not,
what are the scalars in 26#8?
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- ...
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That is, the component-wise sum of the squared error.
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- ...texts
-
Actually these should perhaps be called correlation matrices, translated as they are to the origin.
But they are called covariance matrices almost exclusively, and they are not really correlations,
not being scaled to yield correlation coefficients in the unit interval
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- ...properties
- What should these be called? They seem very much like bilinearity, but
I'm not certain that term can be used here, where everything is matrix algebra...
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- ...product
- Though I really think we can...The
situation is really nothing new. It's as though we had a vector in
, and needed to
take its inner product with a vector 
not lying in the same plane. Though we
can't calculate (x,y) directly, x of course has a representation in 
which allows us
to do so.
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- ...Filter
- Also, there's lots
of terrible puns to be made: we must emphasize the importance of remaining Kalman Cool. Be Kalman. Kalman get it. Sorry.
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- ...variables
- Actually, we can only guarantee their
independence if they are Gaussian - else we really should say only orthogonal. Note that
this is entirely sufficient here.
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- ...
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What does this really mean; these spaces are not the same. But they are both subspaces of this larger space.
See Appendix C
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- ...difference
- The symmetric difference is defined as
which is
often also called ``Exclusive Or''
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- ...operations
- This is really a ring in the abstract algebraic sense if we consider
set intersection and union to be our "multiplication" and "addition", respectively
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