Linear Algebra is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorems for linear maps, including eigenvectors and eigenvalues, quadric and hermitian forms, diagonalization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan

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“This is the third edition of this well-known introduction to linear algebra. The main changes, apart from the usual improvements during a new edition, are the number of exercises which has more than doubled, new formatting including color printing, new sections on product spaces, quotient spaces, duality, and the chapter on ‘Operators on Real Vector Spaces’ … . if you liked the

Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Al-Zaytoonah University of Jordan P.O.Box 130 Amman 11733 Jordan Telephone: 00962-6-4291511 00962-6-4291511 Fax: 00962-6-4291432. Email: president@zuj.edu.jo.

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T is one-to-one if and only if the only vector x such that T(x) = 0 is x = 0 . If T is linear, then T(0 V ) = 0 W .

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1.1 Introduction to Systems of Linear Equations (b) 5. We can see that the second and the third equation are multiples of the first: adding times the first equation to the second, then adding the

2. − 9 p + 3 + 4 p + 7 p − 4 p − 4 p. 2 . - 9 p + 3 + 4 p + 7 p - 4 p - 4 p 2.−9p+ 3+4p+ 7p− 4p −4p.

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Determinants: Finding the determinant of a 3x3 matrixWatch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of

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