## Abstract & Linear Algebra Handwritten Notes pdf

Date: 31st Jan 2023

In these “Abstract & Linear Algebra Handwritten 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.

We have provided multiple complete Linear & Abstract Algebra Handwritten Notes pdf for any university student of BCA, MCA, BSc, BTech CSE, MTech branch to enhance more knowledge about the subject and to score better marks in the exam. Students can easily make use of all these Abstract & Linear Algebra Handwritten Notes pdf by downloading them.

Topics in our Linear & Abstract Algebra Handwritten 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. Algebra handwritten notes free
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