Linear Algebra: An Introduction with Concurrent Examples

This is a good, straightforward introduction to linear algebra. The "concurrent examples" approach works well. My main concern is that the geometric aspects of the subject are somewhat slighted. Geometry is treated very briefly (e.g., despite the emphasis on worked examples, there is not a single numerical example of a determination of the distance from a line to a point or from a plane to a point) and quite clumsily (e.g., using the cosine formula to prove a.b=|a||b|cos(theta), p. 108). This hampers the exposition later. For example, Gram--Schmidt is introduced only towards the end where it is prompted by the orthonormal eigenvector-matrix approach to diagonalisation of symmetric matrices, thus belittling its geometric importance. Also, it seems odd to have such an intricate discussion of diagonalisation without ever mentioning its use in finding A^n.