Linear Algebra A Geometric Approach By S Kumaresan Free
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Linear Algebra: A Geometric Approach by S. Kumaresan - A Review
Linear algebra is a branch of mathematics that studies vector spaces, matrices, linear transformations, determinants, eigenvalues, and systems of linear equations. It has many applications in science, engineering, computer science, and other fields. But how can one learn linear algebra in a way that is intuitive, engaging, and rigorous
One possible answer is Linear Algebra: A Geometric Approach by S. Kumaresan, a professor of mathematics at the University of Mumbai. This book is designed for a first course in linear algebra and is intended for undergraduate courses in mathematics. It focuses throughout on geometric explanations to make the student perceive that linear algebra is nothing but analytic geometry of n dimensions.
From the very start, linear algebra is presented as an extension of the theory of simultaneous linear equations and their geometric interpretation is shown to be a recurring theme of the subject. The integration of abstract algebraic concepts with the underlying geometric notions is one of the most distinguishing features of this book â designed to help students in the pursuit of multivariable calculus and differential geometry in subsequent courses.
The book consists of nine chapters, covering topics such as vector spaces, linear independence and bases, linear transformations and matrices, determinants and area, eigenvalues and eigenvectors, inner product spaces and orthogonality, diagonalization and quadratic forms, and applications of linear algebra. Each chapter contains numerous examples, exercises, and historical notes. The book also includes appendices on logic and proof techniques, complex numbers, and trigonometry.
The book has received positive reviews from readers who praised its clarity, conciseness, readability, and pedagogical value. Some reviewers also appreciated its conversational tone and well-constructed writing style that make the material accessible and interesting for students at a variety of levels.
If you are looking for a book that can help you learn linear algebra in a geometric way, you may want to check out Linear Algebra: A Geometric Approach by S. Kumaresan. You can find it on Google Books[^1^] [^2^] or Amazon[^3^].
One of the main advantages of learning linear algebra in a geometric way is that it helps to develop geometric intuition and visualization skills. Geometric intuition is the ability to understand and reason about abstract concepts using concrete and familiar examples from geometry. Visualization skills are the ability to create and manipulate mental images of geometric objects and transformations. These skills are essential for many areas of mathematics and science, such as calculus, differential equations, physics, engineering, computer graphics, and cryptography.
Another benefit of learning linear algebra in a geometric way is that it makes the subject more fun and enjoyable. Geometry is often considered to be one of the most beautiful and elegant branches of mathematics, with many fascinating results and applications. By relating linear algebra to geometry, the book shows how linear algebra can be used to solve geometric problems, such as finding the area of a triangle, the volume of a tetrahedron, the angle between two vectors, the distance between two planes, or the shape of a conic section. The book also illustrates how geometry can be used to motivate and explain linear algebra concepts, such as linear independence, bases, span, rank, nullity, eigenvectors, orthogonality, and diagonalization.
In conclusion, Linear Algebra: A Geometric Approach by S. Kumaresan is a book that teaches linear algebra in a way that emphasizes geometric understanding and appreciation. It is suitable for students who want to learn linear algebra for the first time or review it for further studies. It is also a valuable resource for instructors who want to adopt a geometric approach in their teaching of linear algebra. The book is available on Google Books or Amazon. 061ffe29dd