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Fix typos introduced during formatting changes
Fixed the following typos: - linear_algebra.md: removed extra '.*.' after 'square' and 'symmetric' - linear_algebra.md: removed extra '.l.' after 'diagonal' - sir_model.md: removed extra 'd)' after 'infected)' - von_neumann_model.md: removed extra '.).' after 'consumed)' - von_neumann_model.md: removed extra '****' after 'outputs' - von_neumann_model.md: removed extra 'es' from 'activitieses' → 'activities'
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lectures/linear_algebra.md

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@@ -471,15 +471,15 @@ For obvious reasons, the matrix $A$ is also called a vector if either $n = 1$ or
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In the former case, $A$ is called a **row vector**, while in the latter it is called a **column vector**.
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If $n = k$, then $A$ is called **square**.*.
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If $n = k$, then $A$ is called **square**.
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The matrix formed by replacing $a_{ij}$ by $a_{ji}$ for every $i$ and $j$ is called the **transpose** of $A$ and denoted $A'$ or $A^{\top}$.
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If $A = A'$, then $A$ is called **symmetric**.*.
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If $A = A'$, then $A$ is called **symmetric**.
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For a square matrix $A$, the $i$ elements of the form $a_{ii}$ for $i=1,\ldots,n$ are called the **principal diagonal**.
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$A$ is called **diagonal** if the only nonzero entries are on the principal diagonal.l.
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$A$ is called **diagonal** if the only nonzero entries are on the principal diagonal.
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If, in addition to being diagonal, each element along the principal diagonal is equal to 1, then $A$ is called the **identity matrix** and denoted by $I$.
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lectures/sir_model.md

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@@ -109,7 +109,7 @@ dynamics are
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In these equations,
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* $\beta(t)$ is called the **transmission rate** (the rate at which individuals bump into others and expose them to the virus).
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* $\sigma$ is called the **infection rate** (the rate at which those who are exposed become infected)d)
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* $\sigma$ is called the **infection rate** (the rate at which those who are exposed become infected)
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* $\gamma$ is called the **recovery rate** (the rate at which infected people recover or die).
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* the dot symbol $\dot y$ represents the time derivative $dy/dt$.
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lectures/von_neumann_model.md

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@@ -365,7 +365,7 @@ A pair $(A,B)$ of $m\times n$ non-negative matrices defines
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an economy.
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- $m$ is the number of **activities** (or sectors)
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- $n$ is the number of **goods** (produced and/or consumed).).
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- $n$ is the number of **goods** (produced and/or consumed)
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- $A$ is called the **input matrix**; $a_{i,j}$ denotes the
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amount of good $j$ consumed by activity $i$
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- $B$ is called the **output matrix**; $b_{i,j}$ represents
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- vector $x^\top A$ gives the total amount of **goods used in
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production**
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- vector $x^\top B$ gives **total outputs****
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- vector $x^\top B$ gives **total outputs**
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An economy $(A,B)$ is said to be **productive**, if there exists a
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non-negative intensity vector $x \geq 0$ such
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The $p$ vector implies **cost** and **revenue** vectors
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- the vector $Ap$ tells **costs** of the vector of activities
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- the vector $Bp$ tells **revenues** from the vector of activitieses
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- the vector $Bp$ tells **revenues** from the vector of activities
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Satisfaction of a property of an input-output pair $(A,B)$ called **irreducibility**
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(or indecomposability) determines whether an economy can be decomposed

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