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QR Decomposition Calculator

Decompose any matrix A into an orthogonal matrix Q and an upper-triangular matrix R such that A = QR. Essential for solving least-squares problems, computing eigenvalues, and numerical linear algebra.

Matrix Element (1,1)

Matrix Element (1,2)

Matrix Element (2,1)

Matrix Element (2,2)

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Linear Algebra

Linear System Solver

Solve systems of two or more linear equations simultaneously to find variable values that satisfy all equations at once. Use this when balancing chemical equations, solving circuit problems, or handling any multi-variable algebra.

Coefficient a₁ (first equation)

Coefficient b₁ (first equation)

Constant (first equation)

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Key differences

	QR Decomposition Calculator	Linear System Solver
Category	Linear Algebra	Linear Algebra
Inputs required	4	3
Result	R Matrix Determinant	Solution x₁
What it does	Decompose any matrix A into an orthogonal matrix Q and an upper-triangular matrix R such that A = QR. Essential for solving least-squares problems, computing eigenvalues, and numerical linear algebra.	Solve systems of two or more linear equations simultaneously to find variable values that satisfy all equations at once. Use this when balancing chemical equations, solving circuit problems, or handling any multi-variable algebra.