diff --git a/tutorials/tutorial1_vectors_matrices.ipynb b/tutorials/tutorial1_vectors_matrices.ipynb index f64f290..52ebc86 100644 --- a/tutorials/tutorial1_vectors_matrices.ipynb +++ b/tutorials/tutorial1_vectors_matrices.ipynb @@ -142,7 +142,7 @@ "## 5. Basic operations\n", "\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", "$$\n", "u + v = \\begin{bmatrix} u_1 + v_1 \\\\ u_2 + v_2 \\\\ \\vdots \\\\ u_n + v_n \\end{bmatrix},\n", @@ -180,7 +180,7 @@ "metadata": {}, "source": [ "### 5.2 Scalar multiplication\n", - "For $ \\alpha \\in \\mathbb{R}, v \\in \\mathbb{R}^n $:\n", + "For $\\alpha \\in \\mathbb{R}, v \\in \\mathbb{R}^n$:\n", "\n", "$$\n", "\\alpha v = \\begin{bmatrix} \\alpha v_1 \\\\ \\alpha v_2 \\\\ \\vdots \\\\ \\alpha v_n \\end{bmatrix}.\n", @@ -215,7 +215,7 @@ "metadata": {}, "source": [ "### 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", "$$\n", "A + B = [ a_{ij} + b_{ij} ], \\quad\n", @@ -254,7 +254,7 @@ "metadata": {}, "source": [ "### 5.4 Matrix-Vector multiplication\n", - "For $ A \\in \\mathbb{R}^{m \\times n}, v \\in \\mathbb{R}^n $:\n", + "For $A \\in \\mathbb{R}^{m \\times n}, v \\in \\mathbb{R}^n$:\n", "\n", "$$\n", "(Av)_i = \\sum_{j=1}^n a_{ij} v_j.\n", @@ -290,7 +290,7 @@ "metadata": {}, "source": [ "### 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", "$$\n", "(AB)_{ij} = \\sum_{k=1}^n a_{ik} b_{kj}.\n", @@ -327,7 +327,7 @@ "metadata": {}, "source": [ "### 5.6 Transpose\n", - "For $ A \\in \\mathbb{R}^{m \\times n} $:\n", + "For $A \\in \\mathbb{R}^{m \\times n}$:\n", "\n", "$$\n", "A^T_{ij} = A_{ji}.\n",