CHAPTER 03.09: BINARY OPERATIONS:
Linear combination of matrices Theory In
this segment we will talk about what is a linear combination of matrices. So
let A1 A2 all the way up to Ap - let’s suppose - be
matrices of same size. So what we mean by that is that the number of rows in
A1 A2 all the way to Ap are the same number of
columns - is A1 A2 all the way to Ap are the same. And
let’s suppose K1 K2 all the way up to Kp are
scalars; then K1 times A1 plus K2 times A2 plus all the way up to Kp times Ap is a linear
combination - is a linear combination of these matrices A1 all the way up to
Ap. So that’s how we define the linear combination of matrices. So somebody
gives us a p of matrices A1 A2 all the way Ap and
wants to find a linear combination of those. Then we can take any values of
K1 through Kp and if we add them all up that
becomes a linear combination of those matrices. This concept is important in
solving simultaneous linear equations, in other places, but that’s what the
definition is when we call - when we say hey what does it
mean to say we have a linear combination of matrices. And that’s the
end of this segment. |