* If x, y, W, and V are real-valued random variables and a, b, c, d are constant (" constant " in this context means non-random ), then the following facts are a consequence of the definition of covariance:

where Z is a normalization constant, A is a symmetric positive definite matrix ( inverse covariance matrix a. k. a. precision matrix ) and b is the shift vector.

This method emphasizes the effect of individual column / row pairs on the result, which is a useful point of view with e. g. covariance matrices, where each such pair corresponds to the effect of a single sample point.

Distance correlation and Brownian covariance / Brownian correlation were introduced to address the deficiency of Pearson's correlation that it can be zero for dependent random variables ; zero distance correlation and zero Brownian correlation imply independence.

If the measures of correlation used are product-moment coefficients, the correlation matrix is the same as the covariance matrix of the standardized random variables X < sub > i </ sub > / σ ( X < sub > i </ sub >) for i = 1, ..., n. This applies to both the matrix of population correlations ( in which case " σ " is the population standard deviation ), and to the matrix of sample correlations ( in which case " σ " denotes the sample standard deviation ).

Notationally, these tensors differ from each other by the covariance / contravariance of their indices.

Bringing to bear the lessons of the absolutism / relationalism debate with the powerful mathematical tools invented in the 19th and 20th century, Michael Friedman draws a distinction between invariance upon mathematical transformation and covariance upon transformation.

In ML Beamformers, quadratic penalty functions are used to the spatial covariance matrix and the signal / noise model.

This could lead to estimated correlations having absolute values which are greater than one, and / or a non-invertible covariance matrix.

Now let us consider the more general case where some distinct elements of have known nonzero covariance ( in other words, the errors in the observations are not independently distributed ), and / or the standard deviations of the errors are not all equal.

He completed, for example, the concept of four vectors ; he created the Minkowski diagram for the depiction of space-time ; he was the first to use expressions like world line, proper time, Lorentz invariance / covariance, etc.

The moment of inertia of a cloud of n points with a covariance matrix of is given by

The covariance matrix ( also called the variance-covariance matrix ) of an n × 1 random vector is an n × n matrix whose i, j element is the covariance between the i < sup > th </ sup > and the j < sup > th </ sup > random variables.

The covariance matrix is the expected value, element by element, of the n × n matrix computed as – E ( X )< sup > T </ sup >, where the superscript T refers to the transpose of the indicated vector:

and the ML estimator of the covariance matrix from a sample of n observations is

) The singular value decomposition of X is X = WΣV < sup > T </ sup >, where the m × m matrix W is the matrix of eigenvectors of the covariance matrix XX < sup > T </ sup >, the matrix Σ is an m × n rectangular diagonal matrix with nonnegative real numbers on the diagonal, and the n × n matrix V is the matrix of eigenvectors of X < sup > T </ sup > X.

For random vectors and ( of dimension m and n respectively ) the m × n covariance matrix is equal to

where M is n × p, Ω is p × p and Σ is n × n. There are several ways to define the two covariance matrices.

Given a sample consisting of n independent observations x < sub > 1 </ sub >,..., x < sub > n </ sub > of a p-dimensional random vector X ∈ R < sup > p × 1 </ sup > ( a p × 1 column-vector ), an unbiased estimator of the ( p × p ) covariance matrix

Given a sample of n independent observations x < sub > 1 </ sub >,..., x < sub > n </ sub > of a p-dimensional zero-mean Gaussian random variable X with covariance R, the maximum likelihood estimator of R is given by

If the sample size n is small and the number of considered variables p is large, the above empirical estimators of covariance and correlation are very unstable.

** CISC — move a -> c ; add c += b.

S += f ( b )

a += b ;

( d += m < 3? y --: y-2, 23 * m / 9 + d + 4 + y / 4-y / 100 + y / 400 )% 7 </ tt >

if n > 1: heaps_twomore += 1

n += 1

n += 1

n += 1

4 voll., pp. XVII-521, pp. 555, pp. 536, pp. 572 ; 2224 total pages ; 100 b / w photos ; ISBN 978-0-19-511307-5.

S ( a, b )=( nc + me / m + n, nd + mf / m + n )

Changing x to x / b stretches the graph horizontally by a factor of b. ( think of the x as being dilated )

* 1938 – Allama Muhammad Iqbal, Philosopher and Urdu / Persian poet ( b. 1877 )

The symbol for bit, as a unit of information, is either simply " bit " ( recommended by the ISO / IEC standard 80000-13 ( 2008 )) or lowercase " b " ( recommended by the IEEE 1541 Standard ( 2002 )).

In an " extended model " which includes hot dark matter in the form of neutrinos, then if the " physical baryon density " Ω < sub > b </ sub > h < sup > 2 </ sup > is estimated at about 0. 023 ( this is different from the ' baryon density ' Ω < sub > b </ sub > expressed as a fraction of the total matter / energy density, which as noted above is about 0. 046 ), and the corresponding cold dark matter density Ω < sub > c </ sub > h < sup > 2 </ sup > is about 0. 11, the corresponding neutrino density Ω < sub > v </ sub > h < sup > 2 </ sup > is estimated to be less than 0. 0062.

In other words, b is a unit in the ring Z / aZ of integers modulo a.

The general formula is set out in section 38 ( 1 ), known as the " 7 / 50 formula ", requires: ( a ) assent from both the House of Commons and the Senate ; ( b ) the approval of two-thirds of the provincial legislatures ( at least seven provinces ) representing at least 50 % of the population ( effectively, this would include at least Quebec or Ontario, as they are the most populous provinces ).

This may be followed by the first letter or letters of the title in lower-case, and / or sometimes the letters a, b, c indicating other printings of the same title.

# a daughter, perhaps named Świętosława, perhaps identical to the legendary Sigrid the Haughty ( b. 968 / 72-d. ca.

The front and back covers of Devo's first release, the 45rpm single ( music ) | single " Mongoloid ( song ) | Mongoloid " b / w " Jocko Homo " ( 1977 ), released on the band's Booji Boy Records

In 1976 Devo released their first single Mongoloid b / w Jocko Homo, the B-side of which came from the soundtrack to The Truth About De-Evolution, on their independent label " Booji Boy ", followed in 1977 by the re-working of the Rolling Stones ' "( I Can't Get No ) Satisfaction ".

* http :// chemistry. about. com / b / a / 184556. htm Observe exothermic reactions in a simple experiment

The property ( EF1 ) can be restated as follows: for any principal ideal I of R with nonzero generator b, all nonzero classes of the quotient ring R / I have a representative r with.

The six women sovereigns reigning after Kōgyoku / Saimei were ( b ) Jitō, ( c ) Gemmei, ( d ) Genshō, ( e ) Kōken / Shōtoku, ( f ) Meishō, and ( g ) Go-Sakuramachi.

The two female monarchs before Jitō were ( a ) Suiko and ( b ) Kōgyoku / Saimei.

The five female monarchs before Kōken / Shōtoku were ( a ) Suiko, ( b ) Kōgyoku / Saimei, ( c ) Jitō, ( d ) Gemmei, and ( e ) Genshō ; and the two women sovereigns reigning after Kōken / Shōtoku were ( f ) Meishō, and ( g ) Go-Sakuramachi.