QR Decomposition Calculator

What is QR Decomposition?

QR decomposition (also called QR factorization) is a matrix decomposition that factors a matrix $A$ into a product $A = QR$ where:

$Q$ is an orthogonal matrix ($Q^T Q = I$, where $Q^T$ is the transpose of $Q$)
$R$ is an upper triangular matrix (all entries below the main diagonal are zero)

QR decomposition has numerous applications in numerical linear algebra and scientific computing:

For a matrix $A$ of dimension $m \times n$, QR decomposition exists if:

If these conditions are not satisfied, the decomposition might not exist or might not be unique.

Number of Rows ($m$)

Number of Columns ($n$)

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