{"product_id":"linear-algebra-study-guide","title":"Linear Algebra","description":"\u003ch1 data-end=\"379\" data-start=\"341\"\u003e🔢Linear Algebra — AristoMind Academy\u003c\/h1\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-pre-wrap leading-[1.7]\"\u003e\u003cstrong\u003eMaster vectors, linear maps, eigenvalues, and the spectral theorem — with geometric intuition and problem-focused learning.\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eLinear Algebra is the language of modern mathematics, physics, machine learning, and engineering. Every chapter includes worked examples, exam-style problems, and a concise exam summary so you know exactly what to learn before a test.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e \u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eWhether you're encountering vector spaces for the first time, already deep in a university course, or revisiting the foundations for higher-level work in data science or theoretical physics — this book gives you the \u003cstrong\u003egeometric intuition\u003c\/strong\u003e, \u003cstrong\u003ecareful derivations\u003c\/strong\u003e, and \u003cstrong\u003estep-by-step solutions\u003c\/strong\u003e needed to truly master the subject.\u003cmeta charset=\"utf-8\"\u003e\u003c\/p\u003e\n\u003chr data-end=\"1545\" data-start=\"1542\"\u003e\n\u003ch3 data-end=\"1569\" data-start=\"1547\"\u003e\u003cbr\u003e\u003c\/h3\u003e\n\u003ch1 data-start=\"0\" data-end=\"22\"\u003e📘 What You’ll Learn\u003c\/h1\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e📐 \u003cstrong\u003eVectors \u0026amp; Geometry \u003c\/strong\u003e— Vectors in Rⁿ, dot products, norms, unit vectors, and geometric applications including lines, planes, and spheres in R² and R³.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e🏗️ \u003cstrong\u003eVector Spaces\u003c\/strong\u003e — Subspaces, linear combinations, span, linear independence, bases, dimension, inner product spaces, and orthonormal bases.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e🔄 \u003cstrong\u003eLinear Maps \u0026amp; Matrices\u003c\/strong\u003e — Kernel, image, injectivity, surjectivity, rank, nullity, and the matrix of a linear map.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e✖️ \u003cstrong\u003eMatrix Operations\u003c\/strong\u003e — Addition, scalar multiplication, matrix multiplication, composition of linear maps, and the relationship between composition and matrix products.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e🔁 \u003cstrong\u003eIsomorphisms \u0026amp; Inverses\u003c\/strong\u003e — Invertible functions, basis criteria for isomorphisms, finding matrix inverses (including the general 2×2 formula), change of basis, and the transpose.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e🔍 \u003cstrong\u003eEigenvalues \u0026amp; Eigenvectors\u003c\/strong\u003e — Characteristic polynomials, determinants (2×2 and 3×3), eigenspaces, the trace, and diagonalisation.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e📊 \u003cstrong\u003eEigenvalues in Depth\u003c\/strong\u003e — Similar matrices, eigenvalues of linear maps in both finite and infinite dimensions, and the contrast between those two settings.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e✨ \u003cstrong\u003eThe Spectral Theorem \u003c\/strong\u003e— Orthogonality, the Gram–Schmidt process, QR factorisation, orthogonal projections onto lines and subspaces, and the least squares method.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e🌐 \u003cstrong\u003eApplications\u003c\/strong\u003e — Systems of differential equations, Markov chains and transport planning, principal component analysis, PageRank, vibration analysis in structural engineering, and population dynamics via Leslie matrices.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e📝 \u003cstrong\u003ePractice \u0026amp; Exam Prep\u003c\/strong\u003e — End-of-chapter problems with solutions and concise exam summaries per chapter.\u003c\/p\u003e\n\u003chr data-end=\"1545\" data-start=\"1542\"\u003e\n\u003ch3 data-end=\"1569\" data-start=\"1547\"\u003e📚 What's Included\u003c\/h3\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e\u003cmeta charset=\"utf-8\"\u003e✅ \u003cstrong data-end=\"1609\" data-start=\"1573\"\u003e310+ beautifully formatted pages\u003c\/strong\u003e\u003cbr data-end=\"1612\" data-start=\"1609\"\u003e✅ \u003cstrong data-end=\"1643\" data-start=\"1614\"\u003e160+ fully solved problems\u003c\/strong\u003e\u003cbr data-end=\"1646\" data-start=\"1643\"\u003e✅ \u003cstrong data-end=\"1691\" data-start=\"1648\"\u003e370+ illustrations and diagrams\u003c\/strong\u003e\u003cbr data-end=\"1694\" data-start=\"1691\"\u003e✅ \u003cstrong data-end=\"1739\" data-start=\"1696\"\u003eExam-focused summaries for each chapter\u003c\/strong\u003e\u003cbr data-end=\"1742\" data-start=\"1739\"\u003e✅ \u003cstrong data-end=\"1795\" data-start=\"1744\"\u003eClickable boxed equations for instant reference\u003c\/strong\u003e\u003c\/p\u003e\n\u003chr data-end=\"1800\" data-start=\"1797\"\u003e\n\u003ch3 data-start=\"206\" data-end=\"228\"\u003e💡 Why AristoMind?\u003c\/h3\u003e\n\u003cp\u003e \u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eThis course was created by someone who's been through the same journey — trained at Oxford and now pursuing a PhD in theoretical physics at Queen Mary University of London, a leading research institute in the field. His work focuses on scattering amplitudes and their connection to black hole physics. \u003cmeta charset=\"utf-8\"\u003eYou can learn more on the \u003ca rel=\"noopener\" title=\"About Us\" href=\"https:\/\/aristomind.academy\/pages\/about-us\" target=\"_blank\"\u003eAbout \u003c\/a\u003e\u003ca href=\"#https:\/\/aristomind.academy\/pages\/about-us\" rel=\"noopener\" class=\"\" data-end=\"380\" data-start=\"367\" title=\"About Us\" target=\"_blank\"\u003eUs\u003c\/a\u003e page and the \u003ca href=\"https:\/\/hu1cq2-c1.myshopify.com\/apps\/frequently-asked-questions\" rel=\"noopener\" class=\"\" data-end=\"380\" data-start=\"367\" title=\"FAQ\" target=\"_blank\"\u003eFAQ\u003c\/a\u003e page.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e\u003cem\u003e\"From Physics Olympiad training to my years at Oxford and now deep into PhD research, one lesson has remained constant: real understanding comes from solving problems, not memorizing facts. That's why this course focuses on clear explanations, step-by-step solutions, and exam-focused summaries — to help you truly grasp and retain the material.\u003c\/em\u003e\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e\u003cem\u003eIt's designed for students in physics, engineering, or mathematics who want to build clarity and confidence as they learn.\"\u003c\/em\u003e — Daniel Siretanu, author\u003c\/p\u003e\n\u003chr data-start=\"2376\" data-end=\"2379\"\u003e\n\u003ch2 data-start=\"2898\" data-end=\"2921\"\u003e📦 Format \u0026amp; Delivery\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cmeta charset=\"utf-8\"\u003e📥 \u003cstrong\u003eInstantly available:\u003c\/strong\u003e Access PDF directly after purchase on your favourite device.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003chr data-end=\"3460\" data-start=\"3457\"\u003e\n\u003ch2 data-end=\"3496\" data-start=\"3462\"\u003e🚀 Upgrade your math toolkit today!\u003c\/h2\u003e\n\u003cp\u003e \u003c\/p\u003e\n\u003cp data-end=\"3720\" data-start=\"3644\"\u003e\u003cmeta charset=\"utf-8\"\u003e\u003cspan\u003eClick “\u003cstrong\u003eOpen Sample\u003c\/strong\u003e” to preview the contents, or add to cart to start learning today.\u003c\/span\u003e\u003c\/p\u003e","brand":"AristoMind","offers":[{"title":"Default Title","offer_id":45388833456307,"sku":null,"price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0695\/0004\/3443\/files\/linear-algebra-5237424.png?v=1775832727","url":"https:\/\/aristomind.academy\/products\/linear-algebra-study-guide","provider":"AristoMind","version":"1.0","type":"link"}