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DOC: LQ and LQMarkov docstrings state E[w_t' w_t] = I instead of E[w_t w_t'] = I

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Issue type
Documentation
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Activity status
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Tech stack
python
Domain
documentation

Research direction

The wrong statement sits in the class docstrings of LQ (quantecon/_lqcontrol.py, around lines 46-49) and LQMarkov (around lines 364-367). docs/source/tools/lqcontrol.rst pulls both through autoclass, so the rendered docs show the same text. Correct the prime placement in both docstrings so they read E[w_t w_t'] = I. Done when both docstrings match and quantecon/tests/test_lqcontrol.py still passes.

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Description

documentation

Summary

The LQ and LQMarkov class docstrings say the shocks satisfy E[w_t' w_t] = I, "the j x j identity". docs/source/tools/lqcontrol.rst pulls both docstrings into the API docs via autoclass. Because w_t is j x 1, w_t' w_t is a scalar, so for j > 1 it cannot equal the j x j identity. The intended statement is the outer product E[w_t w_t'] = I, and that is what the code assumes: d is computed from trace(P C C') (LQ, LQMarkov), and compute_sequence draws each w_t as j independent standard normals (LQ, LQMarkov).

What the code does

LQ, lines 46-49 and LQMarkov, lines 364-367 have the same text:

    Here :math:`x` is n x 1, :math:`u` is k x 1, :math:`w` is j x 1 and the
    matrices are conformable for these dimensions.  The sequence :math:`{w_t}`
    is assumed to be white noise, with zero mean and
    :math:`\mathbb{E} [ w_t' w_t ] = I`, the j x j identity.

Suggested fix

Move the prime in both docstrings:

-    :math:`\mathbb{E} [ w_t' w_t ] = I`, the j x j identity.
+    :math:`\mathbb{E} [ w_t w_t' ] = I`, the j x j identity.

This changes only the docstrings, so no numerical output changes. With the change applied to main, quantecon/tests/test_lqcontrol.py passes unchanged. _lqcontrol.py has no docstring examples, so test_docstring_examples.py does not run these docstrings.

Context

Found while verifying #984, the fix for #982.

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