40 / 45 : add 'Visualizing matrices' intro section (heatmap + Hinton)

Foundation viz section between Definition and Comparison, demonstrating
`plt.matshow` (continuous-magnitude story) and the Hinton diagram
(square area = magnitude, color = sign; zero = empty) on the existing
`mat_A`. Hinton helper inlined for Colab self-containment; matches
`60_linear_algebra_2/matshow.py`.

Pays forward to LA2 viz issues — subsequent notebooks can use Hinton
without re-introducing the convention.

Closes #371

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: kwlee2025cpp

40_linear_algebra_1/45_matrix_and_vector_numpy.ipynb

@@ -3,8 +3,8 @@
   {
    "cell_type": "markdown",
    "metadata": {
-    "id": "view-in-github",
-    "colab_type": "text"
+    "colab_type": "text",
+    "id": "view-in-github"
    },
    "source": [
     "<a href=\"https://colab.research.google.com/github/kangwonlee/nmisp/blob/main/40_linear_algebra_1/45_matrix_and_vector_numpy.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>\n"
@@ -88,6 +88,79 @@
     "\n"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 행렬 시각화<br>Visualizing matrices\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "행렬을 그림으로 살펴보는 두 가지 방법이 있다.<br>\n",
+    "There are two complementary ways to visualize a matrix.\n",
+    "\n",
+    "- **히트맵 (Heatmap)** : 각 칸의 값을 색으로 나타낸다. 회전 행렬과 같이 값이 연속적으로 변하는 행렬에 적합하다.<br>\n",
+    "  **Heatmap** (`plt.matshow`) — colors each cell by its value. Best for matrices whose entries vary smoothly (rotations, geometric transforms).\n",
+    "\n",
+    "- **힌튼 도식 (Hinton diagram)** : 각 칸에 정사각형을 그리되, **정사각형의 넓이는 값의 크기에 비례**하고 **색은 부호를 나타낸다** (흰색 = 양수, 검은색 = 음수). 값이 0인 칸은 *문자 그대로 비어 있게* 보이므로, 행렬의 **구조나 희소성 (sparsity)** 이 한눈에 들어온다.<br>\n",
+    "  **Hinton diagram** — draws a square in each cell whose **area is proportional to the magnitude** and whose **color shows the sign** (white = positive, black = negative). Zero entries are *literally empty*, so structure and sparsity become immediately legible.\n",
+    "\n",
+    "아래에서 같은 행렬 `mat_A` 를 두 방법으로 그려 비교해 본다.<br>\n",
+    "Below, the same `mat_A` is drawn both ways for comparison.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Hinton diagram helper\n",
+    "# (also available at 60_linear_algebra_2/matshow.py)\n",
+    "# Reference: matplotlib gallery — hinton_demo.html\n",
+    "def hinton(matrix, max_weight=None, ax=None):\n",
+    "    if ax is None:\n",
+    "        ax = plt.gca()\n",
+    "    if max_weight is None:\n",
+    "        max_weight = 2 ** np.ceil(np.log2(np.abs(matrix).max()))\n",
+    "    ax.patch.set_facecolor('gray')\n",
+    "    ax.set_aspect('equal', 'box')\n",
+    "    ax.xaxis.set_major_locator(plt.NullLocator())\n",
+    "    ax.yaxis.set_major_locator(plt.NullLocator())\n",
+    "    for (y, x), w in np.ndenumerate(matrix):\n",
+    "        color = 'white' if w > 0 else 'black'\n",
+    "        size = np.sqrt(abs(w) / max_weight)\n",
+    "        rect = plt.Rectangle(\n",
+    "            [x - size / 2, y - size / 2], size, size,\n",
+    "            facecolor=color, edgecolor=color,\n",
+    "        )\n",
+    "        ax.add_patch(rect)\n",
+    "    ax.autoscale_view()\n",
+    "    ax.invert_yaxis()\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fig, (ax_heat, ax_hint) = plt.subplots(1, 2, figsize=(10, 4))\n",
+    "\n",
+    "im = ax_heat.matshow(mat_A)\n",
+    "plt.colorbar(im, ax=ax_heat, fraction=0.046, pad=0.04)\n",
+    "ax_heat.set_title('Heatmap')\n",
+    "\n",
+    "hinton(mat_A, ax=ax_hint)\n",
+    "ax_hint.set_title('Hinton diagram')\n",
+    "\n",
+    "plt.tight_layout()\n",
+    "plt.show()\n"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -570,4 +643,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 4
-}
+}