For courses in Advanced Linear Algebra. This top-selling, theorem-proof text presents a careful treatment of the principle topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate. - NEW - Added section on the singular value decomposition. - Discusses the pseudoinverse of a matrix or a linear transformation between finite-dimensional inner product spaces. - NEW - Revised proofs, added examples and exercises. - Improves the clarity of the text and enhances students understanding of it. - Numerous accessible exercises - Enriches and extends the text material. - Offers students a chance to test their understanding by working interesting problems at a reasonable level of difficulty. - Real-world applications throughout. - Reveals to students the power of the subject by demonstrating its practical uses.