Vectors and matrices¶
Chapters 3–4 of the lecture notes. Vectors and linear independence, matrices, determinants and rank; elementary operations and Gaussian elimination, inverse matrix, LU factorization, eigenvalues and Sylvester's criterion.
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3. Vectors
Definition and transpose · Sum of vectors and scalar multiplication · Scalar product · Linear combinations and linear independence
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4.1. Matrices
Definition and transpose · Sum of matrices and scalar multiplication · Matrix product · Special matrices · …
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4.2. Matrix operations
Elementary row and column operations · Effect of elementary operations on the determinant · Gaussian elimination and row echelon form · Pivoting and partial pivoting
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4.3. Inversion of matrices
Properties of the inverse matrix · Computation of the inverse
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4.4. Factorization of matrices
LU factorization · Determinant from the PLU factorization
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4.5. Eigenvalues and eigenvectors
Eigenvalues · Properties of eigenvalues · A complete example with a … matrix · Sylvester's criterion