is Orthogonal Matrix Definition & Examples

1. is Orthogonal Matrix ?
`[[0,1],[1,0]]`

Solution:

A square matrix `A`, such that `A xx A^T = I`, is called an orthogonal matrix, where `I` is an identity matrix and `A^T` is the transpose of matrix `A`.

`A`

	`0`	`1`
	`1`	`0`

`A^T`

	`0`	`1`
	`1`	`0`

	`0`	`1`
	`1`	`0`

`A×(A^T)`

	`0`	`1`
	`1`	`0`

	`0`	`1`
	`1`	`0`

	`0×0+1×1`	`0×1+1×0`
	`1×0+0×1`	`1×1+0×0`

	`0+1`	`0+0`
	`0+0`	`1+0`

	`1`	`0`
	`0`	`1`

`A xx A^T = I`, So `A` is an orthogonal matrix

2. is Orthogonal Matrix ?
`[[4,-3,1],[0,11,-5],[6,9,14]]`

Solution:

A square matrix `A`, such that `A xx A^T = I`, is called an orthogonal matrix, where `I` is an identity matrix and `A^T` is the transpose of matrix `A`.

`A`

`4`	`-3`	`1`
`0`	`11`	`-5`
`6`	`9`	`14`

`A^T`

`4`	`-3`	`1`
`0`	`11`	`-5`
`6`	`9`	`14`

`4`	`0`	`6`
`-3`	`11`	`9`
`1`	`-5`	`14`

`A×(A^T)`

`4`	`-3`	`1`
`0`	`11`	`-5`
`6`	`9`	`14`

`4`	`0`	`6`
`-3`	`11`	`9`
`1`	`-5`	`14`

`4×4-3×-3+1×1`	`4×0-3×11+1×-5`	`4×6-3×9+1×14`
`0×4+11×-3-5×1`	`0×0+11×11-5×-5`	`0×6+11×9-5×14`
`6×4+9×-3+14×1`	`6×0+9×11+14×-5`	`6×6+9×9+14×14`

`16+9+1`	`0-33-5`	`24-27+14`
`0-33-5`	`0+121+25`	`0+99-70`
`24-27+14`	`0+99-70`	`36+81+196`

`26`	`-38`	`11`
`-38`	`146`	`29`
`11`	`29`	`313`

`A xx A^T != I`, So `A` is not an orthogonal matrix

This material is intended as a summary. Use your textbook for detail explanation.
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1. Definition & Examples