Introduction

• Different possible internal stress fields;
• Mode shapes;
• Simplifying coordinate transforms;
• ...

Linear dependence

Vectors are linearly independent if

only when all coefficients are zero.

So you cannot express one base vector in terms of the rest.

Two vectors are linearly dependent if they are along the same line.

Three vectors are linearly dependent if they are in the same plane.

Basis

A basis for an n-dimensional space is any set of n linearly independent vectors in the space.

Any arbitrary vector in the space can be uniquely expressed in terms of the basis:

Span:

• One basis vector spans a line:

  

• two basis vectors span a plane:

  

• three basis vectors span a 3D space:

  

09/26/01 0:00:15