is Skew Symmetric Matrix Definition & Examples

1. is Skew Symmetric Matrix ?
`[[0,2,3],[-2,0,6],[-3,-6,0]]`

Solution:

A square matrix `A=[a_(ij)]` is said to be a skew symmetric if `A = -A^T` i.e. `a_(ij) = -a_(ji)` for all i,j.

Note : In a skew symmetric matrix, all the diagonal elements are always zero.

`A`

`0`	`2`	`3`
`-2`	`0`	`6`
`-3`	`-6`	`0`

`A^T`

`0`	`2`	`3`
`-2`	`0`	`6`
`-3`	`-6`	`0`

`0`	`-2`	`-3`
`2`	`0`	`-6`
`3`	`6`	`0`

`(-1) × (A^T)`

`-1`

`0`	`-2`	`-3`
`2`	`0`	`-6`
`3`	`6`	`0`

`0`	`2`	`3`
`-2`	`0`	`6`
`-3`	`-6`	`0`

Here, `A` and `-A^T` are equal, so `A` is a skew symmetric matrix

2. is Skew Symmetric Matrix ?
`[[1,2,3],[-2,0,6],[-3,-6,0]]`

Solution:

A square matrix `A=[a_(ij)]` is said to be a skew symmetric if `A = -A^T` i.e. `a_(ij) = -a_(ji)` for all i,j.

Note : In a skew symmetric matrix, all the diagonal elements are always zero.

`A`

`1`	`2`	`3`
`-2`	`0`	`6`
`-3`	`-6`	`0`

`A^T`

`1`	`2`	`3`
`-2`	`0`	`6`
`-3`	`-6`	`0`

`1`	`-2`	`-3`
`2`	`0`	`-6`
`3`	`6`	`0`

`(-1) × (A^T)`

`-1`

`1`	`-2`	`-3`
`2`	`0`	`-6`
`3`	`6`	`0`

`-1`	`2`	`3`
`-2`	`0`	`6`
`-3`	`-6`	`0`

Here, `A` and `-A^T` are not equal, so `A` is not a skew symmetric matrix

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