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单词 Covariance matrix
释义

Covariance matrix

中文百科

协方差矩阵

中心为 (0, 0) 的一个二元高斯概率密度函数，协方差矩阵为 [ 1.00, 0.50 ; 0.50, 1.00 ]。
一个左下右上方向标准差为 3，正交方向标准差为 1 的多元高斯分布的样本点。由于 x 和 y 分量共变，x 与 y 的方差不能完全描述该分布；箭头的方向对应的协方差矩阵的特征矢量，其长度为特征值的平方根。
Sample points from a multivariate Gaussian distribution with a standard deviation of 3 in roughly the lower left-upper right direction and of 1 in the orthogonal direction. Because the x and y components co-vary, the variances of x and y do not fully describe the distribution. A 2×2 covariance matrix is needed; the directions of the arrows correspond to the eigenvectors of this covariance matrix and their lengths to the square roots of the eigenvalues.

在统计学与概率论中，共变异数矩阵（也称离差矩阵、方差-协方差矩阵）是一个矩阵，其 i, j 位置的元素是第 i 个与第 j 个随机矢量（即随机变量构成的矢量）之间的共变异数。这是从标量随机变量到高维度随机矢量的自然推广。

英语百科

Covariance matrix 协方差矩阵

A bivariate Gaussian probability density function centered at (0, 0), with covariance matrix [ 1.00, 0.50 ; 0.50, 1.00 ].
Sample points from a multivariate Gaussian distribution with a standard deviation of 3 in roughly the lower left-upper right direction and of 1 in the orthogonal direction. Because the x and y components co-vary, the variances of x and y do not fully describe the distribution. A 2×2 covariance matrix is needed; the directions of the arrows correspond to the eigenvectors of this covariance matrix and their lengths to the square roots of the eigenvalues.
一个左下右上方向标准差为 3，正交方向标准差为 1 的多元高斯分布的样本点。由于 x 和 y 分量共变，x 与 y 的方差不能完全描述该分布；箭头的方向对应的协方差矩阵的特征矢量，其长度为特征值的平方根。

In probability theory and statistics, a covariance matrix (also known as dispersion matrix or variance–covariance matrix) is a matrix whose element in the i, j position is the covariance between the i  and j  elements of a random vector. A random vector is a random variable with multiple dimensions. Each element of the vector is a scalar random variable. Each element has either a finite number of observed empirical values or a finite or infinite number of potential values. The potential values are specified by a theoretical joint probability distribution.
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更新时间：2025/6/17 16:01:51