QR Decomposition Calculator
Decompose matrices into orthogonal Q and upper triangular R matrices
About this calculator
The QR Decomposition Calculator breaks down any matrix into two components: an orthogonal matrix Q and an upper triangular matrix R. This fundamental linear algebra technique is essential for solving linear systems, least squares problems, and eigenvalue computations. QR decomposition is widely used in numerical analysis, computer graphics, machine learning algorithms, and engineering applications where matrix factorization provides computational advantages and numerical stability.
How to use
Enter your matrix elements in the input fields, separating values with spaces or commas for each row. Click the calculate button to perform the QR decomposition. The calculator will display the orthogonal matrix Q and upper triangular matrix R, showing the complete factorization where A = QR.
Frequently asked questions
What matrices can be decomposed using QR?
Any real or complex matrix can undergo QR decomposition, though square matrices are most commonly used in applications.
How is QR decomposition different from LU decomposition?
QR uses orthogonal and triangular matrices, while LU uses lower and upper triangular matrices. QR provides better numerical stability.
What are the main applications of QR decomposition?
QR decomposition is used for solving linear systems, least squares regression, eigenvalue algorithms, and orthogonalization processes in computational mathematics.