- Calculus, Volume 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability
- Tom M. Apostol
- Second Edition
- 1991
- 978-1-119-49676-2
Chapter 1
- Exercises on the axioms and elementary theorems of linear spaces.
- Subspaces of a linear space.
- Dependent and independent sets in a linear space.
- Bases and dimension.
- Components.
- Exercises on subspaces of a linear space.
- Inner Products, Euclidean Spaces. Norms.
- Orthogonality in a Euclidean space.
- Exercises on the inner product.
- Construction of orthogonal sets. The Gram-Schmidt process.
- Orthogonal components. Projections.
- Best approximation of elements in a Euclidean space by elements in a finite-dimensional subspace.
- Exercises on the Gram-Schmidt process, orthogonal components, and approximation of elements.