Branches of Linear Algebra

What is Linear Algebra?

Linear Algebra is a branch of Mathematics that deals with matrices, vectors, finite and infinite spaces. It is the study of vector spaces, linear equations, linear functions, and matrices....

Linear Algebra Topics

Below is the list of important topics in Linear Algebra....

Branches of Linear Algebra

Linear Algebra is divided into different branches based on the difficulty level of topics, which are,...

Elementary Linear Algebra

Elementary Linear algebra covers the topics of basic linear algebra such as Scalars and Vectors, Matrix and matrix operation, etc....

Advanced Linear Algebra

Advanced linear algebra mostly covers all the advanced topics related to linear algebra such as Linear function, Linear transformation, Eigenvectors, and Eigenvalues, etc....

Vector Space in Linear Algebra

A vector space (or linear space) is a collection of vectors, which may be added together and multiplied (“scaled”) by numbers, called scalars. Scalars are often real numbers, but can also be complex numbers. Vector spaces are central to the study of linear algebra and are used in various scientific fields....

Vectors in Linear Algebra

In linear algebra, vectors are fundamental mathematical objects that represent quantities that have both magnitude and direction....

Linear Function

A formal definition of a linear function is provided below:...

Linear Algebra Matrix

A linear matrix in algebra is a rectangular array of integers organized in rows and columns in linear algebra. The letters a, b, c, and other similar letters are commonly used to represent the integers that make up a matrix’s entries.Matrices are often used to represent linear transformation, such as scaling, rotation, and reflection.Its size is determined by the rows and columns that are present.A matrix has three rows and two columns, for instance. A matrix is referred to as be 3×2 matrix, for instance, if it contains three rows and two columns.Matrix basically works on operations including addition, subtraction, and multiplication.The appropriate elements are simply added or removed when matrices are added or subtracted.Scalar multiplication involves multiplying every entry in the matrix by a scalar(a number).Matrix multiplication is a more complex operation that involves multiplying and adding certain entries in the matrices.The number of columns and rows in the matrix determines its size. For instance, a matrix with 4 rows and 2 columns is known as a 4×2 matrix. The entries in the matrix are integers, and they are frequently represented by letters like u, v, and w....

Numerical Linear Algebra

Numerical linear algebra, also called applied linear algebra, explores how matrix operations can solve real-world problems using computers. It focuses on creating efficient algorithms for continuous mathematics tasks. These algorithms are vital for solving problems like least-square optimization, finding Eigenvalues, and solving systems of linear equations. In numerical linear algebra, various matrix decomposition methods such as Eigen decomposition, Single value decomposition, and QR factorization are utilized to tackle these challenges....

Linear Algebra Applications

Linear algebra is ubiquitous in science and engineering, providing the tools for modelling natural phenomena, optimising processes, and solving complex calculations in computer science, physics, economics, and beyond....

Linear Algebra Problems

Here are some solved questions on Linear Algebra to better your understanding of the concept:...

Conclusion of Linear Algebra

Linear algebra is a branch of mathematics that deals with vector spaces and linear mappings between these spaces. Linear algebra serves as a foundational pillar in mathematics with wide-ranging applications across numerous fields. Its concepts, including vectors, matrices, eigenvalues, and eigenvectors, provide powerful tools for solving systems of equations, analyzing geometric transformations, and understanding fundamental properties of linear mappings....

Linear Algebra – FAQs

What is Linear Algebra?...