Covariance matrix is a mathematical representation of
Answers
Step-by-step explanation:
In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. In the matrix diagonal there are variances, i.e., the covariance of each element with itself.
Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions. As an example, the variation in a collection of random points in two-dimensional space cannot be characterized fully by a single number, nor would the variances in the {\displaystyle x} x and {\displaystyle y} y directions contain all of the necessary information; a {\displaystyle 2\times 2} 2\times 2 matrix would be necessary to fully characterize the two-dimensional variation.
Because the covariance of the i-th random variable with itself is simply that random variable's variance, each element on the principal diagonal of the covariance matrix is the variance of one of the random variables. Because the covariance of the i-th random variable with the j-th one is the same thing as the covariance of the j-th random variable with the i-th random variable, every covariance matrix is symmetric. Also, every covariance matrix is positive semi-definite.
The covariance matrix of a random vector {\displaystyle \mathbf {X} } \mathbf {X} is typically denoted by {\displaystyle \operatorname {K} _{\mathbf {X} \mathbf {X} }} {\displaystyle \operatorname {K} _{\mathbf {X} \mathbf {X} }} or {\displaystyle \Sigma } \Sigma .
Covariance matrix is a mathematical representation of shape of a data set.
Step-by-step explanation:
Mathematically, it is the average squared deviation from the mean score. We use the following formula to compute variance.
Covariance matrix is a mathematical representation of shape of a data set.
Variance measures the variation of a single random variable (like the height of a person in a population),
whereas covariance is a measure of how much two random variables vary together (like the height of a person and the weight of a person in a population).
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How to calculate covariance using covariance matrix?
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