Guia docente 2023_24 Centro Universitario de la Defensa de la Escuela Naval Militar de Marín

Contents

Topic	Sub-topic
Topic 1 (Algebra). Matrices and systems of linear equations	Matrices. Operations. Elementary matrices. Echelon and reduced echelon forms. Rank of a matrix. Invertible matrices. Calculation of the inverse matrix. Determinant of a square matrix. Properties and calculation. Homogeneous and non-homogeneous systems. Existence of solutions.
Topic 2 (Algebra). Vectorial spaces and linear applications	Vector space and subspace. Generator systems. Linear independence. Basis and dimension. Systems of coordinates. Change of basis. Linear applications. Associated matrix. Kernel and rank of a linear application.
Topic 3 (Algebra). Eigenvalues and eigenvectors	Eigenvalues and eigenvectors. Characteristic equation. Diagonalizable matrices. Characteristic polynomial. Cayley-Hamilton theorem. Matrix functions. Exponential matrix of a square matrix.
Topic 4 (Algebra). Vectorial spaces with scalar product. Quadratic forms	Vector spaces with scalar product. Orthogonality. Orthonormal basis. Gram-Schmidt orthogonalization procedure. Orthogonal diagonalization of symmetric matrices. Real quadratic forms. Classification. Sylvester criterion.
Topic 1 (Statistics). Descriptive statistic and regression	Concept and uses of statistics. Variables and attributes. Types of variables. Representations and charts. Measures of location or position. Measures of dispersion. Analysis of bivariant data. Linear regression. Correlation.
Topic 2 (Statistics). Probability	Concept and properties. Conditioned probability and independence of events. Bayes Theorem.
Topic 3 (Statistics). Discrete and continuous random variables	Concept. Types. Probability distribution function of a random variable. Discrete and continuous random variables. Characteristics of a random variable. Remarkable distributions: Binomial, geometric, Poisson, hypergeometric, uniform, exponential, normal. Central limit theorem
Topic 4 (Statistics). Statistical inference	General concepts. Sampling distributions. Estimation. Confidence interval estimate. Hypothesis testing.