Construct an orthogonal matrix using the skew- symmetric matrix `A=[[0,2],[-2,0]].`

Construct an orthogonal matrix using the
skew- symmetric matrix `A=[[0,2],[-2,0]].`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

Salim Ahmed Kawsar

`because A=[[0,2],[-2,0]] rArr I - A = [[1, -2],[2,1]]`
`rArr (I-A)^(-1) =1/5[[1, 2],[-2,1]] and (I+A) = [[1, 2],[-2,1]]`
Let B be the orthogonal matrix from a skew- symmetric
matirx A, then `B= (I-A)^(-1) (I+A)`
` =1/5[[1, 2],[-2,1]] [[1, 2],[-2,1]]=1/5 [[-3,4],[-4,-3]]=[[-3/5,4/5],[-4/5,-3/5]]`

5 views Answered 2023-02-05 15:29

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