Interactive Linear Algebra and its associated software are course materials for introductory linear algebra. The software consists of around 75 (and growing) highly visual online apps that are fully self-contained. Immersed in each app, students make problem-solving decisions in real time, while the software handles routine, low-level calculations to show the outcome of each decision. Students are unencumbered by tedious “pencil and paper” calculations that STEM professionals haven't used for decades, and focus on rapid problem-solving skills. Traditional exercises involving technology simply refer students to “black box” computational software, while the Interactive Linear Algebra software keeps students fully engaged in the mathematical processes they are learning. This engagement leads to better retention of problem-solving strategies and deeper mathematical insight. Interactive Linear Algebra includes standard introductory topics from basic matrix algebra to Singular Value Decomposition. The development of these topics is mathematically rigorous, but the proofs are often inspired by mathematical insights that are imbued by the software. This strategy allows instructors to choose an emphasis on formal proofs that matches the learning objectives of their course. Covers all standard topics in basic linear algebra in a mathematically rigorous way. Permits a broad range of emphasis on mathematical logic and proofs. Allows students to carry out problem-solving steps in real time via immersive apps that handle routine arithmetic and immediately provide the numerical outcome of each student’s decisions. Promotes retention of problem-solving strategies and mathematical insight. Avoids the need for computational software training in class. Saves significant class time, replacing tedious hand-calculations by instructors with brief demonstrations of the self-contained apps. Interactive Linear Algebra is intended for use in introductory linear algebra courses for students pursuing STEM degrees. The text allows any level of emphasis on mathematical rigor, from light treatment to a formal introduction to mathematical proofs. The software, including demos, is available at https://themathatlas.com/