![]() Since a matrix is an array of numbers which can be thought of an array of ordered vectors (either column vectors or row vectors). The operation of the multiplication of a matrix by a real number produces a matrix which keeps its main properties such as: order, linear dependence, proportion between its elements and equivalency between sets of linear equations that may conform it. But as we have said it, we are interested on the case in which a scalar multiplies a matrix.Īnd so, a scalar multiplication of a matrix happens to produce a similar effect when compared to the multiplication of a scalar and a vector. The name "scalar" comes from that particular operation because multiplying a real number by a vector "re-scales" the vector without changing other of its main characteristics, such as direction and dimensions. Remember that a scalar is a real number that multiplied to a vector space it "resizes" the vector (changes its magnitude) without affecting its direction. We are of course, focused on the cases multiplying scalars and matrices together given that we are working on operations with matrices. ![]() The scalar multiplication refers to the operation in which a real number multiplies an algebraic object such as a vector or a matrix. Given that a scalar multiplication is a very simple operation and we have already discussed it before, this section may seem a little redundant but we are keeping so you don't have to be clicking back and forth between this and past lessons if you ever want to see the basic concepts. Now it is time to look in details at the properties this simple, yet important, operation applies. During our lesson about scalar multiplication, we talked about the big differences between this kind of operation and the matrix multiplication.
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