Diabetes happens when one of the following occurs: 1  When the pancreas does not produce any insulin. 2  When the pancreas produces very little insulin. 3  When the body does not respond appropriately to insulin, a condition called insulin resistance..
Vector Calculus: Understanding the Dot Product. Think of the dot product as directional multiplication. Multiplication goes beyond repeated counting: it's applying the essence of one item to another. Complex multiplication combines rotations.
Inner Product. An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. More precisely, for a real vector space, an inner product satisfies the following four properties. Let , , and be vectors and be a scalar, then: