Matrices

Matrices are key concepts in mathematics, widely used in solving equations and problems in fields like physics and computer science. A matrix is simply a grid of numbers, and a determinant is a value calculated from a square matrix.

Example: \begin{bmatrix} 6 & 9 \\ 5 & -4 \\ \end{bmatrix}_{2\times 2}, \begin{bmatrix} 3 & -4 & 5 \\ 1 & 7 & 6 \\ 6 & -2 & 9 \\\end{bmatrix}_{3 \times3}

Matrices for School Students & Beginners

This section covers the basics of matrices, including types, operations, determinants, inverses, and their use in solving equations and real-life applications.

• Introduction to Matrix
• Types of Matrices
• Operations on Matrices
  • Matrix Addition
  • Matrix Subtraction
  • Matrix Multiplication by a Scalar
  • Matrices Multiplication
  • Transpose of a Matrix
• Determinant of a Matrix
• Properties of Determinants
• Determinant of a Matrix Formula
• Invertible Matrix
• Inverse of a Matrix
• Methods to Find Inverse of a Matrix
• How to Solve a System of Equations using Inverse of Matrices
• Transformation Matrix
• Solve Systems of Equations Using Matrices
• Augmented Matrix
• Real-life application of Matrices

Practice Questions on Matrices

This section provides practice questions on matrices, including matrix multiplication and the application of key matrix formulas.

• Matrix Formulas
• Practice Questions on Matrix Multiplication
• Practice Questions on Matrices

Advanced Topics on Matrices

This section explores advanced matrix concepts, including the rank and trace of a matrix, Cramer's rule, covariance matrix, and eigen decomposition, along with eigenvalues, eigenvectors, and partition matrices.

• Rank of Matrix
• Trace of Matrix
• Cramer's Rule
• Covariance Matrix
• Eigen Decomposition of a Matrix
• Eigenvalues and Eigenvectors
• Partition Matrix

Matrices for Programmers

This section covers matrix operations and algorithms for programmers, including tasks like rotating a matrix, multiplying matrices, and solving problems such as finding islands or calculating the maximum sum submatrix. It also delves into advanced topics like matrix chain multiplication and path counting with constraints.

• Matrix Operations
• Rotate Matrix Clockwise
• Sort the given matrix
• Program to multiply two matrices
• Find the row with the maximum number of 1s
• Boundary elements of a Matrix
• Check if a matrix is a Toeplitz Matrix
• Print a given matrix in spiral form
• Zigzag (or diagonal) traversal of Matrix
• Spiral Traversal of Matrix
• Search in a Row-wise and Column-wise Sorted Matrix
• Find the number of islands
• Maximum sum rectangular submatrix in a given matrix
• Minimum Initial Points to Reach Destination
• Count the number of paths with at-most k turns
• Matrix Chain Multiplication

1. Linear Algebra | Introduction of Matrices

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1. Linear Algebra | Introduction of Matrices

Matrices: Definition, Properties, Types, Formulas, and Examples

Adjoint of a Matrix

Determinant of a Matrix- Formula, Properties, Examples, and FAQs

Inverse of a Matrix | Definition, Formula, Examples and Problems

Matrix Multiplication | Step-by-Step Guide, Rules, and Solved Examples

Rank of a Matrix: Definition, Properties, and Formula

Transpose of Matrix - Formula, Examples & How to Find the Transpose

The Covariance Matrix

L U Decomposition of a System of Linear Equations

Eigenvalues & Eigenvectors: Definition, Formula, Examples

What is the Rank of a Matrix? Formula and Examples