linear algebra, a coefficient matrix is a matrix consisting of the coefficients of the variables in a set of linear equations. The matrix is used in solving...

§ Leading term, coefficient and monomial. In linear algebra, a system of linear equations is frequently represented by its coefficient matrix. For example...

if the rank of the augmented matrix ( A | B ) {\displaystyle (A\vert B)} is greater than the rank of the coefficient matrix A {\displaystyle A} . If, on...

In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is...

In mathematics, a matrix coefficient (or matrix element) is a function on a group of a special form, which depends on a linear representation of the group...

expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the column...

incidence matrix of a bipartite graph, which is the coefficient matrix for bipartite matching, is totally unimodular (TU). (The unoriented incidence matrix of...

evaluate a confusion matrix is the Matthews correlation coefficient (MCC). Other metrics can be included in a confusion matrix, each of them having their...

multivariate regression are parameterized by a matrix of coefficients. In the Frobenius inner product above, each matrix X {\displaystyle X} is X i t = e t ⊗ x...

describing the confusion matrix of true and false positives and negatives by a single number, the Matthews correlation coefficient is generally regarded...

is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. If on the other hand, the ranks of these two...

In statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variation in the dependent variable...

system of linear equations, given the ranks of its augmented matrix and coefficient matrix. The theorem is variously known as the: Rouché–Capelli theorem...

consistent if and only if the coefficient matrix has the same rank as its augmented matrix (the coefficient matrix with an extra column added, that column...

product matrix WH is a linear combination of the 10 column vectors in the features matrix W with coefficients supplied by the coefficients matrix H. This...

all the above in reverse. Taking the DCT coefficient matrix (after adding the difference of the DC coefficient back in) [ − 26 − 3 − 6 2 2 − 1 0 0 0 −...

In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices...

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...

taking up much less bandwidth than a full quantizer matrix. This is an example of DCT coefficient matrix: [ − 415 − 33 − 58 35 58 − 51 − 15 − 12 5 − 34 49...

of correlation used are product-moment coefficients, the correlation matrix is the same as the covariance matrix of the standardized random variables X...

{\displaystyle v} is zero, we can eliminate the associated rows of the coefficient matrix without any changes to the rest of the output vector. If v {\displaystyle...

a matrix-free method is an algorithm for solving a linear system of equations or an eigenvalue problem that does not store the coefficient matrix explicitly...

Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant...

eigenvalues as roots. It has the determinant and the trace of the matrix among its coefficients. The characteristic polynomial of an endomorphism of a finite-dimensional...

corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse...

)}{\sum _{j=1}^{N}\mathbf {C} _{ij}}}\end{aligned}}} where coupling coefficient matrix and its cofactors are defined as K = [ 1 k 12 ⋯ k 1 N k 12 1 ⋯ k 2...

>2} ⁠. The best known lower bound for matrix-multiplication complexity is Ω(n2 log(n)), for bounded coefficient arithmetic circuits over the real or complex...

themselves, the inverse of the correlation matrix R x x {\displaystyle R_{xx}} accounts for this. The squared coefficient of multiple correlation can also be...

\theta _{n}}}.\ } In this case the Fisher information matrix may be identified with the coefficient matrix of the normal equations of least squares estimation...

is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. If, on the other hand, the ranks of these two...