{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Tools and Techniques\n", "\n", "This section of the course contains foundational mathematical and statistical\n", "tools and techniques." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lectures\n", "\n", "- [Linear Algebra](linear_algebra.html)\n", " - [Overview](linear_algebra.html#overview)\n", " - [Vectors](linear_algebra.html#vectors)\n", " - [Matrices](linear_algebra.html#matrices)\n", " - [Solving Systems of Equations](linear_algebra.html#solving-systems-of-equations)\n", " - [Eigenvalues and Eigenvectors](linear_algebra.html#eigenvalues-and-eigenvectors)\n", " - [Further Topics](linear_algebra.html#further-topics)\n", " - [Exercises](linear_algebra.html#exercises)\n", " - [Solutions](linear_algebra.html#solutions)\n", "- [Orthogonal Projections and Their Applications](orth_proj.html)\n", " - [Overview](orth_proj.html#overview)\n", " - [Key Definitions](orth_proj.html#key-definitions)\n", " - [The Orthogonal Projection Theorem](orth_proj.html#the-orthogonal-projection-theorem)\n", " - [Orthonormal Basis](orth_proj.html#orthonormal-basis)\n", " - [Projection Using Matrix Algebra](orth_proj.html#projection-using-matrix-algebra)\n", " - [Least Squares Regression](orth_proj.html#least-squares-regression)\n", " - [Orthogonalization and Decomposition](orth_proj.html#orthogonalization-and-decomposition)\n", " - [Exercises](orth_proj.html#exercises)\n", " - [Solutions](orth_proj.html#solutions)\n", "- [LLN and CLT](lln_clt.html)\n", " - [Overview](lln_clt.html#overview)\n", " - [Relationships](lln_clt.html#relationships)\n", " - [LLN](lln_clt.html#lln)\n", " - [CLT](lln_clt.html#clt)\n", " - [Exercises](lln_clt.html#exercises)\n", " - [Solutions](lln_clt.html#solutions)\n", "- [Linear State Space Models](linear_models.html)\n", " - [Overview](linear_models.html#overview)\n", " - [The Linear State Space Model](linear_models.html#the-linear-state-space-model)\n", " - [Distributions and Moments](linear_models.html#distributions-and-moments)\n", " - [Stationarity and Ergodicity](linear_models.html#stationarity-and-ergodicity)\n", " - [Noisy Observations](linear_models.html#noisy-observations)\n", " - [Prediction](linear_models.html#prediction)\n", " - [Code](linear_models.html#code)\n", " - [Exercises](linear_models.html#exercises)\n", " - [Solutions](linear_models.html#solutions)\n", "- [Finite Markov Chains](finite_markov.html)\n", " - [Overview](finite_markov.html#overview)\n", " - [Definitions](finite_markov.html#definitions)\n", " - [Simulation](finite_markov.html#simulation)\n", " - [Marginal Distributions](finite_markov.html#marginal-distributions)\n", " - [Irreducibility and Aperiodicity](finite_markov.html#irreducibility-and-aperiodicity)\n", " - [Stationary Distributions](finite_markov.html#stationary-distributions)\n", " - [Ergodicity](finite_markov.html#ergodicity)\n", " - [Computing Expectations](finite_markov.html#computing-expectations)\n", " - [Exercises](finite_markov.html#exercises)\n", " - [Solutions](finite_markov.html#solutions)\n", "- [Continuous State Markov Chains](stationary_densities.html)\n", " - [Overview](stationary_densities.html#overview)\n", " - [The Density Case](stationary_densities.html#the-density-case)\n", " - [Beyond Densities](stationary_densities.html#beyond-densities)\n", " - [Stability](stationary_densities.html#stability)\n", " - [Exercises](stationary_densities.html#exercises)\n", " - [Solutions](stationary_densities.html#solutions)\n", " - [Appendix](stationary_densities.html#appendix)\n", "- [A First Look at the Kalman Filter](kalman.html)\n", " - [Overview](kalman.html#overview)\n", " - [The Basic Idea](kalman.html#the-basic-idea)\n", " - [Convergence](kalman.html#convergence)\n", " - [Implementation](kalman.html#implementation)\n", " - [Exercises](kalman.html#exercises)\n", " - [Solutions](kalman.html#solutions)\n", "- [Numerical Linear Algebra and Factorizations](numerical_linear_algebra.html)\n", " - [Overview](numerical_linear_algebra.html#overview)\n", " - [Factorizations](numerical_linear_algebra.html#factorizations)\n", " - [Continuous-Time Markov Chains (CTMCs)](numerical_linear_algebra.html#continuous-time-markov-chains-ctmcs)\n", " - [Banded Matrices](numerical_linear_algebra.html#banded-matrices)\n", " - [Implementation Details and Performance](numerical_linear_algebra.html#implementation-details-and-performance)\n", " - [Exercises](numerical_linear_algebra.html#exercises)\n", "- [Krylov Methods and Matrix Conditioning](iterative_methods_sparsity.html)\n", " - [Overview](iterative_methods_sparsity.html#overview)\n", " - [Ill-Conditioned Matrices](iterative_methods_sparsity.html#ill-conditioned-matrices)\n", " - [Stationary Iterative Algorithms for Linear Systems](iterative_methods_sparsity.html#stationary-iterative-algorithms-for-linear-systems)\n", " - [Krylov Methods](iterative_methods_sparsity.html#krylov-methods)\n", " - [Iterative Methods for Linear Least Squares](iterative_methods_sparsity.html#iterative-methods-for-linear-least-squares)\n", " - [Iterative Methods for Eigensystems](iterative_methods_sparsity.html#iterative-methods-for-eigensystems)\n", " - [Krylov Methods for Markov-Chain Dynamics](iterative_methods_sparsity.html#krylov-methods-for-markov-chain-dynamics)" ] } ], "metadata": { "date": 1591310627.559151, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "index.rst", "filename_with_path": "tools_and_techniques/index", "kernelspec": { "display_name": "Julia 1.4.2", "language": "julia", "name": "julia-1.4" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.4.2" }, "title": "Tools and Techniques" }, "nbformat": 4, "nbformat_minor": 2 }