Enter the matrix details into the calculator to determine its pseudoinverse.
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Pseudoinverse Calculation Formula
The pseudoinverse of a matrix is calculated using various methods depending on the properties of the matrix. The following formula is commonly used for calculating the Moore-Penrose pseudoinverse:
A+ = (ATA)-1AT
Variables:
- A+ is the pseudoinverse of matrix A
- AT is the transpose of matrix A
- (ATA)-1 is the inverse of the product of the transpose of matrix A and matrix A
To calculate the pseudoinverse, multiply the transpose of the matrix by the matrix itself, find the inverse of this product, and then multiply by the transpose of the original matrix.
What is Pseudoinverse Calculation?
Pseudoinverse calculation refers to finding a matrix that can serve as a generalized inverse for matrices that are not necessarily invertible. This is particularly useful in solving systems of linear equations that do not have a unique solution or in the context of least squares optimization problems. The Moore-Penrose pseudoinverse is the most widely known and used pseudoinverse.