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Matrix QR Decomposition Calculator

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

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θ

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ddx

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qr decomposition (

1	2
3	4

)

Solution

Q=(

1√10	3√10
3√10	−1√10

), R=(

√10	6√2√5 +√25
0	√25

)

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Solution steps

One step at a time

(

1	2
3	4

)

Multiply by the identity matrix

1	2
3	4

)(

1	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√10	2
3√10	4

)(

√10	0
0	1

)

Orthonormalize column C₂

1√10	3√10
3√10	−1√10

)(

√10	6√2√5 +√25
0	√25

)

Therefore

Q=(

1√10	3√10
3√10	−1√10

), R=(

√10	6√2√5 +√25
0	√25

)

Matrix QR Decomposition Examples

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1	2
3	4

) oder wählen Sie unten

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Notebook

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

1	−1	0
1	0	1
0	−1	1

1	1	1	2
1	0	1	−1
0	−1	−2	1
0	2	0	2

Matrix QR Decomposition Calculator

Solution

Solution steps

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