# QR Decomposition Matrix Calculator

The below online matrix solver helps you to calculate orthogonal matrix (Q) and an upper triangular matrix (R) using QR Decomposition method. It is also referred to as QR Factorization. QR decomposition is often used to solve the linear least squares problem, and is the basis for the QR algorithm. QR decomposition is also called as QR factorization of a matrix. It is denoted as A = QR, where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning QTQ = I) and R is an upper triangular matrix. The QR decomposition can be also be defined as the Gram-Schmidt procedure applied to the columns of the matrix, and with the result expressed in matrix form.

## Calculate Orthogonal Matrix Q and Upper Triangular Matrix R

The below online matrix solver helps you to calculate orthogonal matrix (Q) and an upper triangular matrix (R) using QR Decomposition method. It is also referred to as QR Factorization. QR decomposition is often used to solve the linear least squares problem, and is the basis for the QR algorithm. QR decomposition is also called as QR factorization of a matrix. It is denoted as A = QR, where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning QTQ = I) and R is an upper triangular matrix. The QR decomposition can be also be defined as the Gram-Schmidt procedure applied to the columns of the matrix, and with the result expressed in matrix form.

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#### Formula:

A = QR
R = Q^{T} A
**Where,**
A - Square Matrix
Q - Orthogonal Matrix
R - Upper Triangular Matrix
The basic goal of the QR decomposition is to factor a matrix as a product of two matrices (traditionally called Q,R, hence the name of this factorization). Each matrix has a simple structure which can be further exploited in dealing with, say, linear equations.