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 - letís 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 letís 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 thatís 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 thatís 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 thatís the end of this segment.