QR Factorization Results

Original Matrix (A):

[[1, 2], [3, 4]]

Orthogonal Matrix (Q):

[[-0.3162, -0.9487], [-0.9487, 0.3162]]

Upper Triangular Matrix (R):

[[-3.1623, -4.4272], [0, -0.6325]]
Verification (Q × R = A) expand_more
[[1, 2], [3, 4]]
Step-by-Step Calculation expand_more

1. Initialize Q as a copy of A

2. For each column in Q:

a. Make it orthogonal to all previous columns

b. Normalize the column

3. Calculate R as Qᵀ × A

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