In mathematical terms, the principal components of the distribution of faces or the eigenvectors of the

covariance matrix of the set of face images, is sought by treating an image as a vector in a very high dimensional face space.

The fixed curve was modeled by second and third order polynomial regressions using 12 matrix structures of the random variance and

covariance matrix (G), maintaining the residual effects matrix (R) always equal to the VC.

The inverse of the asymptotic

covariance matrix given (EQUATION)

In contrast, in blind channel estimation, the

covariance matrix of the received signal vectors is exploited to estimate the channel coefficients [5].

X] is the posteriori

covariance matrix of the state parameters; Q is the

covariance matrix of the processing noise; K is the gain matrix of the Kalman filter; H is the coefficient matrix of the observation equation; P is the observation weight matrix; R is the observation noise variance matrix, such that R = [P.

Then, the

covariance matrix of sample matrix is calculated by the following formula:

Investors who know their VaR limit, expected security returns, and the

covariance matrix of those asset returns, can plug those into closed form solutions for portfolio weights, portfolio expected returns, and portfolio standard deviation.

It is convenient to assume that the error term et is Gaussian with mean 0 and

covariance matrix [[OMEGA].

Where Cov_mat in this equation is the estimation

covariance matrix after post-priori estimation.

Section IV shows the market risk premium in CAPM is decided by the expected excess rate of return on assets and the invertible

covariance matrix among the assets' rate of return.

T] is said to have the N-variate t distribution with degree of freedom [mu] with zero mean and R denoting

covariance matrix.

We examine this issue by comparing forecasts of the

covariance matrix obtained by means of a multivariate version of Corsi's Heterogeneous Auto-Regressive (HAR) model with the ones provided by traditional volatility models.

Given the above specification, the BEKK (p,q) model, with the conditional

covariance matrix [H.

t] is related to the conditional variance and

covariance matrix.

The

covariance matrix (14) is diagonal, thus it is assumed that the components of vector [X.