Matrices are essential for the numerical analysis of multivariate series, such as the EEG, and are very useful in solving systems of linear equations. The concept of linear dependence is important and will be discussed initially. Later, the concept and properties of matrices are defined, as well as the main operations that can be performed with them, such as addition, subtraction, product, and inverse matrix. Some elements that characterize or are derived from matrices will be discussed, such as the trace, the determinant, or the concept of positive semidefinite matrix. The concept of generalized inverse matrix will be discussed, which will be essential for the analysis of current source images. Finally, the concepts of eigenvectors and eigenvalues are briefly discussed.

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Linear Algebra: Matrices

  • Jesús Pastor

摘要

Matrices are essential for the numerical analysis of multivariate series, such as the EEG, and are very useful in solving systems of linear equations. The concept of linear dependence is important and will be discussed initially. Later, the concept and properties of matrices are defined, as well as the main operations that can be performed with them, such as addition, subtraction, product, and inverse matrix. Some elements that characterize or are derived from matrices will be discussed, such as the trace, the determinant, or the concept of positive semidefinite matrix. The concept of generalized inverse matrix will be discussed, which will be essential for the analysis of current source images. Finally, the concepts of eigenvectors and eigenvalues are briefly discussed.