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A measure of the number of linearly independent rows or columns in a matrix. It's used in statistics to determine the multivariate normal distribution's degrees of freedom.

The sum of the elements on the main diagonal of a square matrix. Traces in statistics can be used in the expectation calculation of random matrices' quadratic forms.

A non-zero vector that changes at most by its scale factor when a linear transformation is applied. Used in factor analysis and PCA in statistics.

A square matrix with ones on the diagonal and zeros elsewhere, representing the identity transformation. It's central in statistical algorithms that involve matrix inverses or solving linear systems.

A decomposition of a Hermitian, positive-definite matrix into a product of a lower triangular matrix and its conjugate transpose. Useful for efficient numerical solutions in statistics, like simulating multivariate normal distributions.

A scalar value that describes the volume scaling factor of the linear transformation represented by the matrix and can indicate if a system of linear equations has a unique solution. Used in statistics for matrix-based methods like computing multivariate distributions.

A matrix that is equal to its transpose, hence a_ij = a_ji. Symmetric matrices often arise in the study of covariance matrices in statistics.

A matrix decomposition which writes a matrix as the product of a lower and an upper triangular matrix. It's useful in statistical computing for solving linear equations and inverting matrices.

A rectangular array of numbers arranged in rows and columns that can represent a data set or transformations in space. Used in statistics for multivariate analysis and linear models.

Orthogonal vectors that have been normalized to have unit length. These vectors are used in statistics for simplifying the understanding of the structure of data, particularly in PCA.

A scalar value that, when multiplied by a vector, does not change the direction of the vector, only scales it. Important in Principal Component Analysis (PCA) for reducing dimensionality.

A matrix that, when multiplied by the original matrix, yields the identity matrix. Inverse matrices are important in statistics for solving linear equations and calculating coefficients in linear regression.

When no vector in a set is a linear combination of the others, providing unique information. This concept ensures that data or model features are not redundant.

A set of vectors that are linearly independent and span a vector space. In statistics, bases are used to define coordinate systems or reference frames for data.

A matrix where the entries outside the main diagonal are all zero. In statistics, diagonalization simplifies computations in methods like diagonalizing covariance matrices for PCA.

A factorization of a matrix into three components: a rotation, a scaling, and another rotation. SVD is used in statistical methods like PCA for dimensionality reduction.

All possible vectors that can be reached through linear combinations of a set of vectors. In statistics, it helps understand the range of values that can be derived from a set of factors.

An algorithm for orthogonalizing a set of vectors in an inner product space, resulting in an orthonormal set. It's applied in statistics for regression diagnostics and Orthogonal Least Squares.

An ordered list of numbers that can represent points in space, weights for averages, or coefficients in regression. Often used as a random variable in multivariate statistics.

Vectors that, when dotted together, yield zero, indicating they are at right angles. In statistics, orthogonality is central to decorrelating variables and simplifying models.

A matrix representing the covariance between each pair of elements in a random vector, often used to understand the dispersion and correlation in multivariate data.

A combination of multiple vectors scaled by coefficients leading to a new vector. Employed in regression analysis to predict outcomes.

A method of estimating the coefficients of a linear model by minimizing the sum of squares of the residuals. Fundamental in regression analysis for fitting models to data.

A set of vectors that form a space closed under addition and scalar multiplication. In statistics, subspaces are used in hypothesis testing and constructing confidence intervals.