Quantum computing explained in terms of elementary linear algebra emphasizing computation & algorithms & requiring no background in physics This introduction to quantum algorithms is concise but comprehensive covering many key algorithms It is mathematically rigorous but requires minimal background & assumes no knowledge of quantum theory or quantum mechanics The book explains quantum computation in terms of elementary linear algebra; it assumes the reader will have some familiarity with vectors matrices & their basic properties but offers a review of all the relevant material from linear algebra By emphasizing computation & algorithms rather than physics this primer makes quantum algorithms accessible to students & researchers in computer science without the complications of quantum mechanical notation physical concepts & philosophical issues After explaining the development of quantum operations & computations based on linear algebra the book presents the major quantum algorithms from seminal algorithms by Deutsch Jozsa & Simon through Shor's & Grover's algorithms to recent quantum walks It covers quantum gates computational complexity & some graph theory Mathematical proofs are generally short & straightforward; quantum circuits & gates are used to illuminate linear algebra; & the discussion of complexity is anchored in computational problems rather than machine models Quantum Algorithms via Linear Algebra is suitable for classroom use or as a reference for computer scientists & mathematicians