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    "\n",
    "<a id='tools-and-techniques'></a>\n",
    "<div id=\"qe-notebook-header\" style=\"text-align:right;\">\n",
    "        <a href=\"https://quantecon.org/\" title=\"quantecon.org\">\n",
    "                <img style=\"width:250px;display:inline;\" src=\"https://assets.quantecon.org/img/qe-menubar-logo.svg\" alt=\"QuantEcon\">\n",
    "        </a>\n",
    "</div>"
   ]
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   "source": [
    "# Tools and Techniques\n",
    "\n",
    "This section of the course contains foundational mathematical and statistical\n",
    "tools and techniques"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "## Lectures\n",
    "\n",
    "- [Linear Algebra](linear_algebra.ipynb)\n",
    "  - [Overview](linear_algebra.ipynb#overview)\n",
    "  - [Vectors](linear_algebra.ipynb#vectors)\n",
    "  - [Matrices](linear_algebra.ipynb#matrices)\n",
    "  - [Solving Systems of Equations](linear_algebra.ipynb#solving-systems-of-equations)\n",
    "  - [Eigenvalues and Eigenvectors](linear_algebra.ipynb#eigenvalues-and-eigenvectors)\n",
    "  - [Further Topics](linear_algebra.ipynb#further-topics)\n",
    "  - [Exercises](linear_algebra.ipynb#exercises)\n",
    "  - [Solutions](linear_algebra.ipynb#solutions)\n",
    "- [Orthogonal Projections and Their Applications](orth_proj.ipynb)\n",
    "  - [Overview](orth_proj.ipynb#overview)\n",
    "  - [Key Definitions](orth_proj.ipynb#key-definitions)\n",
    "  - [The Orthogonal Projection Theorem](orth_proj.ipynb#the-orthogonal-projection-theorem)\n",
    "  - [Orthonormal Basis](orth_proj.ipynb#orthonormal-basis)\n",
    "  - [Projection Using Matrix Algebra](orth_proj.ipynb#projection-using-matrix-algebra)\n",
    "  - [Least Squares Regression](orth_proj.ipynb#least-squares-regression)\n",
    "  - [Orthogonalization and Decomposition](orth_proj.ipynb#orthogonalization-and-decomposition)\n",
    "  - [Exercises](orth_proj.ipynb#exercises)\n",
    "  - [Solutions](orth_proj.ipynb#solutions)\n",
    "- [LLN and CLT](lln_clt.ipynb)\n",
    "  - [Overview](lln_clt.ipynb#overview)\n",
    "  - [Relationships](lln_clt.ipynb#relationships)\n",
    "  - [LLN](lln_clt.ipynb#lln)\n",
    "  - [CLT](lln_clt.ipynb#clt)\n",
    "  - [Exercises](lln_clt.ipynb#exercises)\n",
    "  - [Solutions](lln_clt.ipynb#solutions)\n",
    "- [Linear State Space Models](linear_models.ipynb)\n",
    "  - [Overview](linear_models.ipynb#overview)\n",
    "  - [The Linear State Space Model](linear_models.ipynb#the-linear-state-space-model)\n",
    "  - [Distributions and Moments](linear_models.ipynb#distributions-and-moments)\n",
    "  - [Stationarity and Ergodicity](linear_models.ipynb#stationarity-and-ergodicity)\n",
    "  - [Noisy Observations](linear_models.ipynb#noisy-observations)\n",
    "  - [Prediction](linear_models.ipynb#prediction)\n",
    "  - [Code](linear_models.ipynb#code)\n",
    "  - [Exercises](linear_models.ipynb#exercises)\n",
    "  - [Solutions](linear_models.ipynb#solutions)\n",
    "- [Finite Markov Chains](finite_markov.ipynb)\n",
    "  - [Overview](finite_markov.ipynb#overview)\n",
    "  - [Definitions](finite_markov.ipynb#definitions)\n",
    "  - [Simulation](finite_markov.ipynb#simulation)\n",
    "  - [Marginal Distributions](finite_markov.ipynb#marginal-distributions)\n",
    "  - [Irreducibility and Aperiodicity](finite_markov.ipynb#irreducibility-and-aperiodicity)\n",
    "  - [Stationary Distributions](finite_markov.ipynb#stationary-distributions)\n",
    "  - [Ergodicity](finite_markov.ipynb#ergodicity)\n",
    "  - [Computing Expectations](finite_markov.ipynb#computing-expectations)\n",
    "  - [Exercises](finite_markov.ipynb#exercises)\n",
    "  - [Solutions](finite_markov.ipynb#solutions)\n",
    "- [Continuous State Markov Chains](stationary_densities.ipynb)\n",
    "  - [Overview](stationary_densities.ipynb#overview)\n",
    "  - [The Density Case](stationary_densities.ipynb#the-density-case)\n",
    "  - [Beyond Densities](stationary_densities.ipynb#beyond-densities)\n",
    "  - [Stability](stationary_densities.ipynb#stability)\n",
    "  - [Exercises](stationary_densities.ipynb#exercises)\n",
    "  - [Solutions](stationary_densities.ipynb#solutions)\n",
    "  - [Appendix](stationary_densities.ipynb#appendix)\n",
    "- [A First Look at the Kalman Filter](kalman.ipynb)\n",
    "  - [Overview](kalman.ipynb#overview)\n",
    "  - [The Basic Idea](kalman.ipynb#the-basic-idea)\n",
    "  - [Convergence](kalman.ipynb#convergence)\n",
    "  - [Implementation](kalman.ipynb#implementation)\n",
    "  - [Exercises](kalman.ipynb#exercises)\n",
    "  - [Solutions](kalman.ipynb#solutions)"
   ]
  }
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