I just finished Matrices and Linear Algebra by Schneider & Barker, and I found it pretty good. I'm now looking for another book to strengthen my understanding of the subject. I intend to use the book for self-study just like I did using this one. I narrowed down my choices to two books: An Introduction to Linear Algebra by L. Mirsky and Linear Algebra by G. Shilov, but I don't know which one to pick. Here are their TOCs: An Introduction to Linear Algebra - L. Mirksy Part 1 - Determinants, Vectors, Matrices, and Linear Eqations I. Determinants II. Vector Spaces and Linear Manifolds III. The Algebra of Matrices IV. Linear Operators V. Systems of Linear Equations and Rank of Matrices VI. Elementary Operations and the Concept of Equivalence Part 2 - Further Development of Matrix Theory VII. The Characteristic Equation VIII. Orthogonal and Unitary Matrices IX. Groups X. Canonical Forms XI. Matrix Analysis Part 3 - Quadratic Forms XII. Bilinear, Quadratic, and Hermitian Forms XIII. Definite and Indefinite Forms Linear Algebra - G. Shilov I. Determinants II. Linear Spaces III. Systems of Linear Equations IV. Linear Functions of a Vector Argument V. Coordinate Transformations VI. The Canonical Form of the Matrix of a Linear Operator VII. Bilinear and Quadratic Forms VIII. Euclidean Spaces IX. Unitary Spaces X. Quadratic Forms in Euclidean and Unitary Spaces XI. Finite-Dimensional Algebras and their Representations I'd appreciate any help. And if you pick one, could you please explain your choice? I'm also open to other suggestions, but please keep in mind the following: 1. I'm on a very limited budget 2. I'm only a high school senior, so nothing too advanced! Thank you.