## Abstract & Linear Algebra Notes PDF

Free Abstract & Linear Algebra notes pdf are provided here for Abstract & Linear Algebra students so that they can prepare and score high marks in their Abstract & Linear Algebra exam.

In these free Abstract & Linear Algebra notes pdf, we will study the basic tools of theory of equations, complex numbers, number theory, and matrices to understand their connection with real-world problems. Perform matrix algebra with applications to computer graphics.

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Topics in our Abstract & Linear Algebra Notes PDF

The topics we will cover in these Linear & Abstract Algebra Handwritten Notes pdf will be taken from the following list:

Theory of Equations and Complex Numbers: Polynomials, The remainder and factor theorem, Synthetic division, Factored form of a polynomial, Fundamental theorem of algebra, Relations between the roots and the coefficients of polynomial equations, Theorems on imaginary, integral and rational roots; Polar representation of complex numbers, De Moivre’s theorem for integer and rational indices and their applications. The nth roots of unity.

Equivalence Relations and Functions: Equivalence relations, Functions, Composition of functions, Invertibility, and inverse of functions, One-to-one correspondence, and the cardinality of a set.

Basic Number Theory: Well ordering principle, The division algorithm in Z, Divisibility, and the Euclidean algorithm, Fundamental theorem of arithmetic, Modular arithmetic, and basic properties of congruences; Principle of mathematical induction.

Row Echelon Form of Matrices and Applications: Systems of linear equations, Row reduction, and echelon forms, Vector equations, The matrix equation Ax = b, Solution sets of linear systems, The inverse of a matrix; Subspaces, Linear independence, Basis and dimension, The rank of a matrix and applications; Introduction to linear transformations, The matrix of a linear transformation; Applications to computer graphics, Eigenvalues and eigenvectors, The characteristic equation and Cayley-Hamilton theorem.

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## Abstract & Linear Algebra Notes FAQs

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