Introduction to Computational Linear Algebra

6 Introduction to Computational Linear Algebra

Operation Vector-Vector Component MATLAB

Notation Notation Implementation

Scalar-Vector

Multiplication z = ax z

i

= ax

i

z=a*x

Vector Addition z = x + y z

i

= x

i

+ y

i

z=x+y

saxpy z = ax + y z

i

= ax

i

+ y

i

z=a*x+y

scalar product a = x

T

y a =

P

i

x

i

y

i

z=x’*y

Hadamard vector

multiply

(component-wise) z = x .× y z

i

= x

i

y

i

z=x.*y

TABLE 1.2: Basic vector-vector operations.

In this table, saxpy means “scalar a ? x plus y”; it is not independent of the

preceding two operations, but it is common to list it as a basic operation

because it occurs frequently in practical calculations.

The analysis of complexity would go as follows. By denoting ...