Hi everyone,

The question I am trying to solve is as follows:

"ax is the matrix operator that, when operating on any other vector, produces the effect of cross product of that vector with the vector a. That is axb = a X b for any vector b. Show that ax^2 = aaT - |a|^2I"

where:

"^2" means squared

"ax" is a subscript x

"a X b" means 'a' cross product 'b'

"aT" is 'a-transpose'

I understand |a|^2 to equal a1^2 + a2^2 + a3^3 + ... (i.e. first element of a squared, plus second element of a squared, plus ... etc). Is this correct?

What does ax^2 mean? Is it simply a X a (cross product)?

Can someone please provide a little insight as to what the above expression (both left and right sides) actually means.

Thank you.