Concept

Cramer's rule

Related lectures (17)

Linear Algebra: Determinants and Applications

Explores determinants, similarity invariance, Cramer's formula, and geometric interpretations in matrices.

Determinants: Expansion Theorems and Cramer's Formula

Covers the expansion theorems for determinants and introduces Cramer's formula.

Cramer's Rule

Covers Cramer's Rule for solving linear equations using determinants and column replacements.

Linear Algebra: Cramer's Rule

Covers Cramer's Rule for solving linear equations using determinants.

Cramer's Rule and Volume

Covers Cramer's Rule, matrix inverse, determinants, and volume in linear algebra.

Geometric Quantization

Explores geometric quantization, the process of quantizing classical systems to obtain quantum systems using mathematical techniques like pseudo-differential calculus.

Cramer's Rule and Matrix Inverse

Covers Cramer's Rule for solving linear equations and calculating matrix inverses.

Cramer's Rule and Matrix Inverse

Explores Cramer's Rule for solving linear equations and calculating matrix inverses.

Linear Algebra: Applications and Algorithms

Explores applications of linear algebra in image and signal processing, and introduces algorithms like Gaussian elimination and LU decomposition.

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Determinant Calculation and Cramer's Rule

Covers the calculation of determinants and Cramer's rule for matrix invertibility.

Linear Applications: Matrices and Matrix Calculations

Explores linear applications, associated matrices, and matrix operations in the context of injective and surjective maps.

Matrix Operations: Rules and Applications

Covers matrix operations, including multiplication, transposition, powers, and inverses, and explains how to determine if a matrix is invertible.

Hilbert Spaces: Definition and Properties

Covers the definition and properties of Hilbert spaces, including the Cauchy-Schwarz inequality and norm definition.

Characterization of totally unimodular matrices

Explores equitable coloring in totally unimodular matrices, enabling integral vectors and bicoloring results.

Ideal MHD Waves

Covers the concept of Ideal MHD waves and the behavior of plasma under different conditions.

Vector Calculus: Direct Frame

Explores the concept of a direct frame in vector calculus and its properties, emphasizing the importance of understanding fundamental vector concepts.