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some typos for math in tutorial1

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Ömür Uğur
2025-09-17 12:30:58 +03:00
parent f73789bca6
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1 changed files with 6 additions and 6 deletions
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tutorials/tutorial1_vectors_matrices.ipynb
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@@ -142,7 +142,7 @@
"## 5. Basic operations\n", "## 5. Basic operations\n",
"\n", "\n",
"### 5.1 Vector addition and subtraction\n", "### 5.1 Vector addition and subtraction\n",
"For $ u, v \\in \\mathbb{R}^n $:\n", "For $u, v \\in \\mathbb{R}^n$:\n",
"\n", "\n",
"$$\n", "$$\n",
"u + v = \\begin{bmatrix} u_1 + v_1 \\\\ u_2 + v_2 \\\\ \\vdots \\\\ u_n + v_n \\end{bmatrix},\n", "u + v = \\begin{bmatrix} u_1 + v_1 \\\\ u_2 + v_2 \\\\ \\vdots \\\\ u_n + v_n \\end{bmatrix},\n",
@@ -180,7 +180,7 @@
"metadata": {}, "metadata": {},
"source": [ "source": [
"### 5.2 Scalar multiplication\n", "### 5.2 Scalar multiplication\n",
"For $ \\alpha \\in \\mathbb{R}, v \\in \\mathbb{R}^n $:\n", "For $\\alpha \\in \\mathbb{R}, v \\in \\mathbb{R}^n$:\n",
"\n", "\n",
"$$\n", "$$\n",
"\\alpha v = \\begin{bmatrix} \\alpha v_1 \\\\ \\alpha v_2 \\\\ \\vdots \\\\ \\alpha v_n \\end{bmatrix}.\n", "\\alpha v = \\begin{bmatrix} \\alpha v_1 \\\\ \\alpha v_2 \\\\ \\vdots \\\\ \\alpha v_n \\end{bmatrix}.\n",
@@ -215,7 +215,7 @@
"metadata": {}, "metadata": {},
"source": [ "source": [
"### 5.3 Matrix addition and subtraction\n", "### 5.3 Matrix addition and subtraction\n",
"For $ A, B \\in \\mathbb{R}^{m \\times n} $:\n", "For $A, B \\in \\mathbb{R}^{m \\times n}$:\n",
"\n", "\n",
"$$\n", "$$\n",
"A + B = [ a_{ij} + b_{ij} ], \\quad\n", "A + B = [ a_{ij} + b_{ij} ], \\quad\n",
@@ -254,7 +254,7 @@
"metadata": {}, "metadata": {},
"source": [ "source": [
"### 5.4 Matrix-Vector multiplication\n", "### 5.4 Matrix-Vector multiplication\n",
"For $ A \\in \\mathbb{R}^{m \\times n}, v \\in \\mathbb{R}^n $:\n", "For $A \\in \\mathbb{R}^{m \\times n}, v \\in \\mathbb{R}^n$:\n",
"\n", "\n",
"$$\n", "$$\n",
"(Av)_i = \\sum_{j=1}^n a_{ij} v_j.\n", "(Av)_i = \\sum_{j=1}^n a_{ij} v_j.\n",
@@ -290,7 +290,7 @@
"metadata": {}, "metadata": {},
"source": [ "source": [
"### 5.5 Matrix-Matrix multiplication\n", "### 5.5 Matrix-Matrix multiplication\n",
"For $ A \\in \\mathbb{R}^{m \\times n}, B \\in \\mathbb{R}^{n \\times p} $:\n", "For $A \\in \\mathbb{R}^{m \\times n}, B \\in \\mathbb{R}^{n \\times p}$:\n",
"\n", "\n",
"$$\n", "$$\n",
"(AB)_{ij} = \\sum_{k=1}^n a_{ik} b_{kj}.\n", "(AB)_{ij} = \\sum_{k=1}^n a_{ik} b_{kj}.\n",
@@ -327,7 +327,7 @@
"metadata": {}, "metadata": {},
"source": [ "source": [
"### 5.6 Transpose\n", "### 5.6 Transpose\n",
"For $ A \\in \\mathbb{R}^{m \\times n} $:\n", "For $A \\in \\mathbb{R}^{m \\times n}$:\n",
"\n", "\n",
"$$\n", "$$\n",
"A^T_{ij} = A_{ji}.\n", "A^T_{ij} = A_{ji}.\n",