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A similarity transformation which preserves orientation, also called a homothety.

Two variates A and B are statistically independent iff the conditional probability P(A|B) of A given B satisfies P(A|B)=P(A), (1) in which case the probability of A and B is ...

The L^2-inner product of two real functions f and g on a measure space X with respect to the measure mu is given by <f,g>_(L^2)=int_Xfgdmu, sometimes also called the bracket ...

2^(20)=1024^2=1048576 bytes. Although the term megabyte is almost universally used to refer to 1024^2 bytes, such usage is deprecated in favor of the standard SI naming ...

If a compact manifold M has nonnegative Ricci curvature tensor, then its fundamental group has at most polynomial growth. On the other hand, if M has negative curvature, then ...

The unit of information obtained by using the natural logarithm lnx instead of the base-2 logarithm log_2x=lgx when defining entropy and related information theoretic ...

The operation of interchanging true and false in a logical statement. The negation of A is often called "NOT-A," and can be denoted !A, or with the negation sign ¬, so not-A ...

In a space E equipped with a symmetric, differential k-form, or Hermitian form, the orthogonal sum is the direct sum of two subspaces V and W, which are mutually orthogonal. ...

If f(x) is a monotonically increasing integrable function on [a,b] with f(b)<=0, then if g is a real function integrable on [a,b], ...

Li and Yorke (1975) proved that any one-dimensional system which exhibits a regular cycle of period three will also display regular cycles of every other length as well as ...