Álgebra lineal y los fundamentos del aprendizaje profundo, ¡juntos por fin! Del profesor Gilbert Strang, aclamado autor de Introducción al álgebra lineal, llega Álgebra lineal en ciencia de datos, el primer libro de texto que enseña álgebra lineal junto con aprendizaje profundo y redes neuronales. Este libro de texto ameno pero riguroso contiene un curso completo de álgebra lineal y de la matemática relacionada que los estudiantes deben saber para familiarizarse con el aprendizaje a partir de los datos. Se incluyen: los cuatro subespacios fundamentales, descomposición en valores singulares, matrices especiales, técnicas de cálculo con matrices grandes, compressed sensing, probabilidad y estadística, optimización, arquitectura de redes neuronales, descenso por gradiente estocástico y retropropagación.
Este manual se propone cubrir plenamente los temas de álgebra lineal que requieren los profesionales y estudiantes de Ciencias Económicas como base para el desarrollo de otras áreas como la investigación de operaciones, entre otras. Para ello se presentan los conceptos básicos de matrices, determinantes, sistemas de ecuaciones lineales. Ademas, se incluye talleres para desarrollar en Matlab, con el fin de fortalecer los conceptos básicos, así como ejemplos de aplicación y ejercicios relativos a temas económicos y financieros.
If you want to work in any computational or technical field, you need to understand linear algebra. As the study of matrices and operations acting upon them, linear algebra is the mathematical basis of nearly all algorithms and analyses implemented in computers. But the way it's presented in decades-old textbooks is much different from how professionals use linear algebra today to solve real-world modern applications. This practical guide from Mike X Cohen teaches the core concepts of linear algebra as implemented in Python, including how they're used in data science, machine learning, deep learning, computational simulations, and biomedical data processing applications. Armed with knowledge from this book, you'll be able to understand, implement, and adapt myriad modern analysis methods and algorithms. Ideal for practitioners and students using computer technology and algorithms, this book introduces you to: The interpretations and applications of vectors and matrices Matrix arithmetic (various multiplications and transformations) Independence, rank, and inverses Important decompositions used in applied linear algebra (including LU and QR) Eigendecomposition and singular value decomposition Applications including least-squares model fitting and principal components analysis
If you want to work in any computational or technical field, you need to understand linear algebra. As the study of matrices and operations acting upon them, linear algebra is the mathematical basis of nearly all algorithms and analyses implemented in computers. But the way it's presented in decades-old textbooks is much different from how professionals use linear algebra today to solve real-world modern applications. This practical guide from Mike X Cohen teaches the core concepts of linear algebra as implemented in Python, including how they're used in data science, machine learning, deep learning, computational simulations, and biomedical data processing applications. Armed with knowledge from this book, you'll be able to understand, implement, and adapt myriad modern analysis methods and algorithms. Ideal for practitioners and students using computer technology and algorithms, this book introduces you to: The interpretations and applications of vectors and matrices Matrix arithmetic (various multiplications and transformations) Independence, rank, and inverses Important decompositions used in applied linear algebra (including LU and QR) Eigendecomposition and singular value decomposition Applications including least-squares model fitting and principal components analysis.
Álgebra lineal y sus aplicaciones constituye un texto planeado y diseñado especialmente para todos los alumnos universitarios que estudian cursos semestrales o anuales de esta asignatura, debido a que se concibe como un texto flexible que se ajusta a los tiempos y necesidades académicas de cada institución. Durante su realización, los autores siempre tuvieron en mente el futuro de los estudiantes como profesionistas, por lo que el principal propósito de esta obra es ofrecerle todas las herramientas cuantitativas que pueda aplicar en la solución de diversos problemas a que se enfrentará en su ámbito académico y laboral, y que lo apoyarán a una mejor toma de decisiones. Con base en esta premisa, a lo largo de todo el libro el lector encontrará diversas aplicaciones a diferentes áreas, entre las que destacan la administración, la ingeniería, las finanzas, la económica, las ciencias sociales, la informática, entre muchas otras.
This groundbreaking textbook combines straightforward explanations with a wealth of practical examples to offer an innovative approach to teaching linear algebra. Requiring no prior knowledge of the subject, it covers the aspects of linear algebra - vectors, matrices, and least squares - that are needed for engineering applications, discussing examples across data science, machine learning and artificial intelligence, signal and image processing, tomography, navigation, control, and finance. The numerous practical exercises throughout allow students to test their understanding and translate their knowledge into solving real-world problems, with lecture slides, additional computational exercises in Julia and MATLAB®, and data sets accompanying the book online. Suitable for both one-semester and one-quarter courses, as well as self-study, this self-contained text provides beginning students with the foundation they need to progress to more advanced study.
El texto, dirigido fundamentalmente a estudiantes de economía de los niveles de licenciatura y posgrado, puede ser utilizado también por profesionales interesados en ampliar las posibilidades de emplear la matemática en sus análisis económicos. Cubre un vasto campo donde se combinan las técnicas operacionales y de cálculo con los conceptos básicos de las estructuras matemáticas que se estudian, prestando atención a los fundamentos teóricos de la disciplina a un nivel que, sin exceder los límites adecuados para un economista, permiten conservar el suficiente rigor analítico. En la exposición se combinan la teoría con ilustraciones de aplicaciones a la economía. De inicio presenta un conjunto de reflexiones sobre el ámbito de la matemática en la economía, que contribuye al debate sobre el papel de la matemática en el desarrollo de la ciencia económica. Siguiendo una secuencia lógica, se estudian las matrices y los sistemas de ecuaciones lineales reales; los espacios lineales reales; las transformaciones lineales, y se concluye con el tema de las transformaciones de semejanza. Desde el inicio se muestran ilustraciones de los conceptos estudiados al análisis económico. Los apéndices a cada capítulo complementan los temas desarrollados en el texto.
Master the math needed to excel in data science, machine learning, and statistics. In this book author Thomas Nield guides you through areas like calculus, probability, linear algebra, and statistics and how they apply to techniques like linear regression, logistic regression, and neural networks. Along the way you'll also gain practical insights into the state of data science and how to use those insights to maximize your career. Learn how to: Use Python code and libraries like SymPy, NumPy, and scikit-learn to explore essential mathematical concepts like calculus, linear algebra, statistics, and machine learning Understand techniques like linear regression, logistic regression, and neural networks in plain English, with minimal mathematical notation and jargon Perform descriptive statistics and hypothesis testing on a dataset to interpret p-values and statistical significance Manipulate vectors and matrices and perform matrix decomposition Integrate and build upon incremental knowledge of calculus, probability, statistics, and linear algebra, and apply it to regression models including neural networks Navigate practically through a data science career and avoid common pitfalls, assumptions, and biases while tuning your skill set to stand out in the job market
This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the underlying linear algebraic techniques, thereby enabling students not only to learn how to apply the mathematical tools in routine contexts, but also to understand what is required to adapt to unusual or emerging problems. No previous knowledge of linear algebra is needed to approach this text, with single-variable calculus as the only formal prerequisite. However, the reader will need to draw upon some mathematical maturity to engage in the increasing abstraction inherent to the subject. Once equipped with the main tools and concepts from this book, students will be prepared for further study in differential equations, numerical analysis, data science and statistics, and a broad range of applications. The first author’s text, Introduction to Partial Differential Equations, is an ideal companion volume, forming a natural extension of the linear mathematical methods developed here.
