Fundamentals of Continuum Mechanics

2.2.4 Cartesian components, indicial notation, summation convention

Every Euclidean space ${\epsilon }^n$ has an orthonormal basis. A basis for ${\epsilon }^n$ is a linearly independent set of vectors that spans ${\epsilon }^n$. Orthonormality implies that each pair of vectors in the set is orthogonal (or perpendicular) to each other, and every vector in the set has unit norm. Three-dimensional Euclidean space ${\epsilon }^3$ has a fixed orthonormal basis {e₁, e₂, e₃}.³ Any vector u in ${\epsilon }^3$ can be expressed ...