Linear Algebra: Quadratic Forms and Matrix Diagonalization

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Explores quadratic forms, symmetric bilinear forms, and their properties.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Covers the theory and applications of bilinear forms in various mathematical contexts.

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.