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HomeHomework HelpmathematicsMatrix Theory

Matrix Theory

Matrix theory is a branch of mathematics that deals with the study of matrices, which are rectangular arrays of numbers, symbols, or expressions, arranged in rows and columns, and the operations that can be performed on them.

intermediate
5 hours
Mathematics
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Overview

Matrix theory is a vital area of mathematics that focuses on the study of matrices and their properties. It provides tools for solving systems of linear equations, performing transformations, and analyzing data. Understanding matrices is essential for various applications in fields like computer gra...

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Key Terms

Matrix
A rectangular array of numbers or symbols arranged in rows and columns.

Example: A = [[1, 2], [3, 4]]

Determinant
A scalar value that is a function of the entries of a square matrix, providing important properties.

Example: For matrix A = [[a, b], [c, d]], det(A) = ad - bc.

Eigenvalue
A scalar that indicates how much a corresponding eigenvector is stretched or compressed during a linear transformation.

Example: If A*v = λ*v, then λ is the eigenvalue.

Eigenvector
A non-zero vector that changes by only a scalar factor when a linear transformation is applied.

Example: In the equation A*v = λ*v, v is the eigenvector.

Linear Transformation
A mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication.

Example: Rotating a vector in 2D space is a linear transformation.

Identity Matrix
A square matrix with ones on the diagonal and zeros elsewhere, acting as the multiplicative identity.

Example: I = [[1, 0], [0, 1]]

Related Topics

Linear Algebra
The study of vector spaces and linear mappings between them.
intermediate
Vector Spaces
A mathematical structure formed by a collection of vectors.
intermediate
Numerical Methods
Techniques for solving numerical problems using matrices and algorithms.
advanced

Key Concepts

MatricesDeterminantsEigenvaluesLinear Transformations