**Alpha Connection**

A non-metric connection is not determined by a metric tensor ; instead, it is and restricted by the requirement that the parallel transport between points and must be a linear combination of the base vectors in . Here,

expresses the parallel transport of as linear combination of the base vectors in, *i.e.* the new minus the change. Note that it is not a tensor (does not transform as a tensor).

For such a metric, one can construct a dual connection to make

- ,

for parallel transport using and .

For the mentioned -families the affine connection is called the -connection and can also be expressed in more ways.

For :

- is a metric connection and with .
- ,
i.e. is dual to with respect to the Fisher metric.

- If this is called -affine. Its dual is then -affine.
, i.e. 0-affine, and hence, i.e. 1-affine.

Read more about this topic: Information Geometry, Introduction

### Famous quotes containing the words connection and/or alpha:

“One must always maintain one’s *connection* to the past and yet ceaselessly pull away from it. To remain in touch with the past requires a love of memory. To remain in touch with the past requires a constant imaginative effort.”

—Gaston Bachelard (1884–1962)

“Imagination is a valuable asset in business and she has a sister, Understanding, who also serves. Together they make a splendid team and business problems dissolve and the impossible is accomplished by their ministrations.... Imagination concerning the world’s wants and the individual’s needs should be the *Alpha* and Omega of self-education.”

—Alice Foote MacDougall (1867–1945)