• Linearity in technology.
• Vector space, linear representation, matrix matrices.
• Rank and defect of linear representations, the composition of linear representations, the principle of superposition.
• Linear mapping matrix, similarity.
• Bilinear and quadratic forms.
• Matrix and classification of bilinear and quadratic forms, congruence, and LDLT decomposition.
• Scalar product and orthogonality.
• Standards, variational principle, least squares method, projectors.
• Combined gradient method.
• Rotation, mirroring, QR decomposition, and system solutions.
• Eigenvalues and vectors, localization of eigenvalues.
• Spectral decomposition of a symmetric matrix and its consequences.
• Symmetric matrix functions, polar decomposition, singular decomposition, and pseudoinverse.
• Jordan's form.
• Vector space, linear representation, matrix matrices.
• Rank and defect of linear representations, the composition of linear representations, the principle of superposition.
• Linear mapping matrix, similarity.
• Bilinear and quadratic forms.
• Matrix and classification of bilinear and quadratic forms, congruence, and LDLT decomposition.
• Scalar product and orthogonality.
• Standards, variational principle, least squares method, projectors.
• Combined gradient method.
• Rotation, mirroring, QR decomposition, and system solutions.
• Eigenvalues and vectors, localization of eigenvalues.
• Spectral decomposition of a symmetric matrix and its consequences.
• Symmetric matrix functions, polar decomposition, singular decomposition, and pseudoinverse.
• Jordan's form.