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(Trick Question: ) What is 0 · u ?


If the "0" is a scalar (which the non-bold type indicates) then this operation makes no sense.

If the "0" means the zero-vector (which means the zero should have been in bold face) then the result is the scalar 0.

Dot Product of Column Matrices

The dot product is also defined for column matrices.

Let a = ( a1, a2 )T
Let b = ( b1, b2 )T

Then the dot product is defined as:

a · b = a1b1 + a2b2

Multiply corresponding elements of each column matrix, then add up the products. The result is a scalar value.

Sometimes the dot product of column matrices is written like this: aT b (but it is defined the same way). The reason for this second, odd notation will be apparent in a later chapter when matrix multiplication is discussed.

Here is an example: