# involutory transformations - why are they not so much used in signal processing? [closed]

We generally prefer orthogonal transformations/matrices in signal processing as the transpose of the matrix is the inverse and you do not need to find inverse transform separately. But involutory matrix is one step ahead. It is the inverse of itself. Why don't we see involutory matrices in signal processing? I am not aware of any involutory matrix used as a transform matrix.

• how's that "one step ahead"? Where's that useful? sorry, I just can't see an overly dramatic use case of that, but I think you might have one in mind; you should probably explain that. – Marcus Müller Jun 26 '16 at 21:39
• orthogonal transforms are advantageous, they say, because inverse you don't have to calculate separately. You just transpose to get the inverse. Involuntary transform is one step ahead in this sense. You don't have to even transpose. The matrix is itself its inverse. – Seetha Rama Raju Sanapala Jun 27 '16 at 7:20
• yeah, but calculating the inverse operation to a transform a never an actual problem – you don't have to do that in real-time, just once, when designing your system. And then, you have all the time you need. And inverting a matrix is not that complex, either. – Marcus Müller Jun 27 '16 at 7:30

• @SeethaRamaRajuSanapala, (linear) involutions are very underpowered, because they can only distinguish two subspaces. The discrete Fourier transform on an $n$-dimensional vector distinguishes $n$ subspaces, making it much more powerful if $n>2$. So you will never find an involution that replaces any sufficiently complicated transform on higher dimensional vector spaces. – Jazzmaniac Jul 5 '16 at 7:37