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"
"^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.