This book on linear algebra and geometry is based on a course given by renowned academician ir shafarevich at moscow state university the book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces linear transformations inner product spaces and the theory of affine and projective spaces. Buy linear algebra and geometry a second course dover books on mathematics on amazoncom free shipping on qualified orders. Linear algebra and geometry we construct a dictionary between some geometrical notions and some notions from linear algebra adding scalar multiplication an element of xy 2r2 corresponds to an arrow with tail at the origin in r2 and head at the point xy two arrows are the same vector if they have the same length and direction. Linear algebra and geometry is organized around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics requiring only high school algebra it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field. A major application of linear algebra is to solving systems of linear equations this lecture presents three ways of thinking about these systems the row method focuses on the individual equations the column method focuses on combining the columns and the matrix method is an even more compact and powerful way of describing systems of
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