# Positive Definite Matrix Calculator Online

#### Results

### Positive Definite Matrix Calculator Description

### Explanation:

If both pre and post multiplication of a square matrix by the same vector always yield positive results,
regardless of the vector we choose, then the square matrix is said to be positive definite.

It is a characteristic of positive definite symmetric matrices that all of their eigenvalues are positive.

**or**

The term "positive definite" refers to a square matrix that is symmetric and has all of its eigenvalues greater
than zero.

#### Properties of Positive Definite Matrix Calculator

- All eigenvalues are positive λ > 0
- All of the upper left determinant of a matrix must be greater than 0
- Every pivot element of the matrix must be greater than 0
- If G is postive definite then S = A
^{T}A (A here must be independent column). - x
^{T}Sx > 0 for all x (other than zero vector)

#### How to use check Positive Definite Matrix Calculator?

- Firstly, you need to enter the dimension of the matrix. Enter number of rows in "Rows" input field and Enter number of columns in "Columns" input field.
- Then press the button "Set Matrix".
- An empty matrix will appear below and then you can enter your values inside the matrix.
- After entering all the values press "Solve" button, the result will automatically appear below which check whether the matrix is Positive Definite Matrix or not.

** Positive Definite Matrix Example Image:**

### More Calculators

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