# What if the covariance matrix is not positive definite?

## What if the covariance matrix is not positive definite?

If a covariance or correlation matrix is not positive definite, then one or more of its eigenvalues will be negative.

## Is the covariance matrix always positive definite?

The covariance matrix is always both symmetric and positive semi- definite.

Can a covariance matrix be negative?

negative correlation between two elements will end up with a corresponding negative entry in the covariance matrix. The negative shapes are shape components with surfece evenness.

### Can covariance matrix have negative eigenvalues?

1 Answer. While in theory an estimated covariance matrix must be positive (semi-)definite, i.e. no negative values, in practice floating-point error can violate this.

### When is the symmetric part of a matrix positive definite?

A symmetric matrix is positive definite if and only if its quadratic form is a strictly convex function . More generally, any quadratic function from is positive definite.

Is the sum of positive definite matrices positive definite?

Yes, Swapnil, the sum of two positive definite matrices is positive definite. Sum of two positive scalars is positive. That is why the sum of the two quadratic forms concerned will have positive terms only.

#### What is the variance-covariance matrix?

A variance-covariance matrix is a square matrix that contains the variances and covariances associated with several variables. The diagonal elements of the matrix contain the variances of the variables and the off-diagonal elements contain the covariances between all possible pairs of variables.

#### Is every positive definite always a symmetric matrix?

A positive deﬁnite matrix is a symmetric matrix with all positive eigenvalues. Note that as it’s a symmetric matrix all the eigenvalues are real, so it makes sense to talk about them being positive or negative. Now, it’s not always easy to tell if a matrix is positive deﬁnite.