Linear Scalar Equations

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Explores linear algebra fundamentals, including key definitions, theorems, and practical applications in mathematics and technology.

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

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Explains linear independence, basis, and matrix rank with examples and exercises.

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Covers the properties and criteria of linear dependence and independence in a vector space.

Explores vector spaces, linear independence, and spanning sets in linear algebra.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.