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: a^T 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:

• a   =   ( 1, 2 )^T
• b   =   ( 3, 4 )^T
• a · b  =  1*3 + 2*4  =  3 + 8  =  11