Julia's

LinearAlgebra

Linear algebra is a branch of mathematics that deals with vectors, vector spaces (also called linear spaces), linear mappings, and systems of linear equations. It is fundamental to many areas of science and engineering, including physics, computer science, and economics.

The

LinearAlgebra

• Matrix Multiplication:
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  *

  operator for standard matrix multiplication.
• Transpose:
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  transpose(A)

  or
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  A'

  for the transpose of a matrix.
• Inverse:
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  inv(A)

  for the matrix inverse.
• Determinant:
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  det(A)

  for the determinant of a square matrix.
• Eigenvalues and Eigenvectors:
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  eigen(A)

  to compute eigenvalues and eigenvectors.
• Singular Value Decomposition (SVD):
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  svd(A)

  for computing the SVD.
• LU Decomposition:
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  lu(A)

  for LU decomposition.
• Cholesky Decomposition:
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  cholesky(A)

  for Cholesky decomposition.

Julia's

LinearAlgebra

The

LinearAlgebra

• Solving Systems of Linear Equations: Crucial for many scientific models.
• Data Fitting and Regression: Techniques like least squares often involve solving linear systems.
• Machine Learning: Many algorithms, such as principal component analysis (PCA) and support vector machines (SVMs), rely heavily on linear algebra.
• Image Processing: Operations like filtering and transformations can be represented using matrices.
• Quantum Mechanics: State vectors and operators are represented using matrices.