Linear Algebra

A branch of mathematics.

Foundations

• Determinant

• Hermitian transpose

• Invertibility

• Matrix conjugation

• Matrix multiplication

• Orthogonality

• Positive definiteness

• Rank

• Special matrices

• Trace

• Transposition

Linear Transformations

• Basis

• Eigenvalues and Eigenvectors

• Idempotency

• Linear mapping

• Linearity

• Rotation matrix

• Singular values

Elimination

• Elimination

• General solution

• Null Space

• Particular solution

• Trivial solution

Decompositions and Factorizations

• Diagonalization

• LU Decomposition

• Orthonormalization

• Quadratic form

• Singular value decomposition

Applications

• Systems of differential equations

• Low rank approximation

• Markov matrices

• Projection

• Pseudoinverse

Inner Product Spaces

• Inner product

• Norm

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CategoryRicottone CategoryMathematics