Essentials of Mechatronics

Chapter 7.4 Transposition Of Matrices

7.4   TRANSPOSITION OF MATRICES

Our mixed fruit multiplication can be written as

 

or equally well as

 

giving 5 oranges + 3 lemons + 2 grapefruit in both cases—this result is in the
form of a scalar. But note that in reversing the order in which we multiply the
vectors, we have had to transpose them.

Transposing a scalar is not very spectacular—but when two matrices are
multiplied together to give another matrix, C = AB, then, if we wish to fi nd
out the transpose of C, we must both transpose A and B and reverse the order
in which we multiply them:

 C' = B'A'

 

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