# Vector Multiplication Rules

This post categorized under Vector and posted on September 16th, 2019.

The right hand rule for cross multiplication relates the direction of the two vectors with the direction of their product. Since cross multiplication is not commutative the order of operations is important. In mathematics matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field or more generally in a ring or even a semiring. How to multiply matrices with vectors and other matrices.

Multiplying a Vector by a Matrix To multiply a row vector by a column vector the row vector must have as many columns as the column vector has rows. Let us define the multiplication between a matrix A and a vector x in which the number of columns in A equals the number of rows in x . When we do multiplication The number of columns of the 1st matrix must equal the number of rows of the 2nd matrix . And the result will have the same number of rows as the 1st matrix and the same number of columns as the 2nd matrix . The multiplication of a vector by a vector produces some interesting results known as the vector inner product and as the vector outer product. Prerequisite This material vectorumes familiarity with matrix multiplication. s is a scalar that is s is a real number - not a matrix. Note this

Vectors - What Are They gives an introduction to the subject. There are two useful definitions of multiplication of vectors in one the product is a scalar and in the other the product is a vector. Unit vectors enable two convenient idenvectories the dot product of two unit vectors yields the cosine (which may be positive or negative) of the angle between the two unit vectors. The magnitude of the cross product of the two unit vectors yields the sine (which will always be positive). Matrix multiplication is not universally commutative for nonscalar inputs. That is AB is typically not equal to BA . If at least one input is scalar then AB is equivavectort to A.B and is commutative. That rule probably seemed fairly stupid at the time because you already knew that order didnt matter in multiplication. Introducing you to those rules back then was probably kind of pointless since order didnt matter for anything you were multiplying then.

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