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Matrix QR Decomposition Calculator

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qr decomposition (

1	1	1	2
1	0	1	−1
0	−1	−2	1
0	2	0	2

)

Solution

Q=(

1√2	1√22	−13√11	23
1√2	−1√22	13√11	−23
0	−√211	−3√11	0
0	2√211	−43√11	−13

), R=(

√2	1√2	√2	1√2
0	√112	2√211	3√211 +3√22
0	0	6√11	−203√11
0	0	0	43

)

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Solution steps

One step at a time

(

1	1	1	2
1	0	1	−1
0	−1	−2	1
0	2	0	2

)

Multiply by the identity matrix

1	1	1	2
1	0	1	−1
0	−1	−2	1
0	2	0	2

)(

1	0	0	0
0	1	0	0
0	0	1	0
0	0	0	1

)

QR Decomposition using Gram-Schmidt Algorithm

Use Gram-Schmidt Algorithm to turn the matrix to orthogonal matrix.
Apply the inverse operations to an identity matrix to get an upper rectangular matrix

Orthonormalize column C₁

1√2	1	1	2
1√2	0	1	−1
0	−1	−2	1
0	2	0	2

)(

√2	0	0	0
0	1	0	0
0	0	1	0
0	0	0	1

)

Orthonormalize column C₂

1√2	1√22	1	2
1√2	−1√22	1	−1
0	−√211	−2	1
0	2√211	0	2

)(

√2	1√2	0	0
0	√112	0	0
0	0	1	0
0	0	0	1

)

Orthonormalize column C₃

1√2	1√22	−13√11	2
1√2	−1√22	13√11	−1
0	−√211	−3√11	1
0	2√211	−43√11	2

)(

√2	1√2	√2	0
0	√112	2√211	0
0	0	6√11	0
0	0	0	1

)

Orthonormalize column C₄

1√2	1√22	−13√11	23
1√2	−1√22	13√11	−23
0	−√211	−3√11	0
0	2√211	−43√11	−13

)(

√2	1√2	√2	1√2
0	√112	2√211	3√211 +3√22
0	0	6√11	−203√11
0	0	0	43

)

Therefore

Q=(

1√2	1√22	−13√11	23
1√2	−1√22	13√11	−23
0	−√211	−3√11	0
0	2√211	−43√11	−13

), R=(

√2	1√2	√2	1√2
0	√112	2√211	3√211 +3√22
0	0	6√11	−203√11
0	0	0	43

)

Matrix QR Decomposition Examples

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Chat with Symbo

こんにちは, について質問する qr decomposition (

1	1	1	2
1	0	1	−1
0	−1	−2	1
0	2	0	2

) または以下を選択してください

−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

Matrix QR Decomposition Calculator

Solution

Solution steps

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