*

content/series/mathematics-for-machine-learning/linear-algebra-fundamentals/en/index.mdx

@@ -253,21 +253,19 @@ r = np.cross(p, q) # [-8  5  1]
 
 A matrix is an array of numbers that are arranged into rows and columns.
 
-```bash
-A = [
-  1 2 3
-  4 5 6
-]
-```
+<BlockMath>{`\\begin{equation}A = \\begin{bmatrix}
+  1 & 2 & 3 \\\\
+  4 & 5 & 6
+ \\end{bmatrix}
+\\end{equation}`}</BlockMath>
 
 This is how you indicate each element in the matrix:
 
-```bash
-A = [
-  a₁,₁  a₁,₂  a₁,₃
-  a₂,₁  a₂,₂  a₂,₃
-]
-```
+<BlockMath>{`\\begin{equation}A = \\begin{bmatrix}
+  a_{1,1} & a_{1,2} & a_{1,3} \\\\
+  a_{2,1} & a_{2,2} & a_{2,3}
+ \\end{bmatrix}
+\\end{equation}`}</BlockMath>
 
 In Python, we can define the matrix as a 2-dimensional array:
 
@@ -282,21 +280,17 @@ A = np.array([[1,2,3],
 
 To add two matrices of the same size together, just add the corresponding elements in each matrix:
 
-```bash
-[               [             [
-  1 2 3     +     6 5 4   =     7 7 7
-  4 5 6           3 2 1         7 7 7
-]               ]             ]
-```
+<BlockMath>
+  {`\\begin{equation}\\begin{bmatrix}1 & 2 & 3 \\\\4 & 5 & 6\\end{bmatrix}+ \\begin{bmatrix}6 & 5 & 4 \\\\3 & 2 & 1\\end{bmatrix} = \\begin{bmatrix}7 & 7 & 7 \\\\7 & 7 & 7\\end{bmatrix}\\end{equation}`}
+</BlockMath>
 
 Here's how we calculate it:
 
-```bash
-[
-  a₁,₁ + b₁,₁, a₁,₂ + b₁,₂, a₁,₃ + b₁,₃
-  a₂,₁ + b₂,₁, a₂,₂ + b₂,₂, a₂,₃ + b₂,₃
-]
-```
+<BlockMath>{`\\begin{equation}A = \\begin{bmatrix}
+  a_{1,1} + b_{1,1} & a_{1,2} + b_{1,2}  & a_{1,3} + b_{1,3}  \\\\
+  a_{2,1} + b_{2,1}  & a_{2,2} + b_{2,2}  & a_{2,3} + b_{2,3} 
+ \\end{bmatrix}
+\\end{equation}`}</BlockMath>
 
 In Python, we can just sum the two matrices:
 
@@ -314,26 +308,19 @@ A + B
 
 Subtraction of two matrices works the same way:
 
-```bash
-[               [             [
-  1 2 3     -     6 5 4   =     -5 -3 -1
-  4 5 6           3 2 1         1   3  5
-]               ]             ]
-```
+<BlockMath>
+  {`\\begin{equation}\\begin{bmatrix}1 & 2 & 3 \\\\4 & 5 & 6\\end{bmatrix}- \\begin{bmatrix}6 & 5 & 4 \\\\3 & 2 & 1\\end{bmatrix} = \\begin{bmatrix}-5 & -3 & -1 \\\\1 & 3 & 5\\end{bmatrix}\\end{equation}`}
+</BlockMath>
 
 The nagative of a matrix, is just a matrix with the sign of each element reversed.
 
-```bash
-C = [
-  -5  -3  -1
-  1   3   5
-]
-
--C = [
-  5   3    1
-  -1  -3   -5
-]
-```
+<BlockMath>
+  {`\\begin{equation}C = \\begin{bmatrix}-5 & -3 & -1 \\\\1 & 3 & 5\\end{bmatrix}\\end{equation}`}
+</BlockMath>
+
+<BlockMath>
+  {`\\begin{equation}-C = \\begin{bmatrix}5 & 3 & 1 \\\\-1 & -3 & -5\\end{bmatrix}\\end{equation}`}
+</BlockMath>
 
 In Python, we can use the minus sign:
 
@@ -351,13 +338,9 @@ C
 
 Matrix Transposition is when we switch the orientation of its rows and columns:
 
-```bash
-[               [
-  1 2 3    =      1 4
-  4 5 6           2 5
-] ͭ                3 6
-                ]
-```
+<BlockMath>
+  {`\\begin{equation}\\begin{bmatrix}1 & 2 & 3 \\\\4 & 5 & 6\\end{bmatrix}^{T} = \\begin{bmatrix}1 & 4\\\\2 & 5\\\\3 & 6 \\end{bmatrix}\\end{equation}`}
+</BlockMath>
 
 In Python, we have the `T` method:
 
@@ -374,12 +357,9 @@ A.T
 
 Scalar multiplication in matrices looks similar to scalar multiplication in vectors. To multiply a matrix by a scalar value, you just multiply each element by the scalar to produce a new matrix:
 
-```bash
-     [                 [
-2 ·     1 2 3     =       2  4   6
-        4 5 6             8  10  12
-     ]                 ]
-```
+<BlockMath>
+  {`\\begin{equation}2 \\times \\begin{bmatrix}1 & 2 & 3 \\\\4 & 5 & 6\\end{bmatrix} = \\begin{bmatrix}2 & 4 & 6 \\\\8 & 10 & 12\\end{bmatrix}\\end{equation}`}
+</BlockMath>
 
 In Python, we simply perform the multiplication of two values:
 
@@ -394,15 +374,9 @@ A = np.array([[1,2,3],
 
 To mulitply two matrices, we need to calculate the dot product of rows and columns.
 
-```bash
-A · B
-
-[               [
-  1 2 3     ·     9 8
-  4 5 6           7 6
-]                 5 4
-                ]
-```
+<BlockMath>
+  {`\\begin{equation}\\begin{bmatrix}1 & 2 & 3 \\\\4 & 5 & 6\\end{bmatrix} \\cdot \\begin{bmatrix}9 & 8 \\\\ 7 & 6 \\\\ 5 & 4\\end{bmatrix}\\end{equation}`}
+</BlockMath>
 
 How to calculate this multiplication:
 
@@ -422,12 +396,9 @@ Resulting in these calculations:
 
 Resulting in this matrix:
 
-```bash
-[
-  38   32
-  101  86
-]
-```
+<BlockMath>
+  {`\\begin{equation}\\begin{bmatrix}38 & 32\\\\101 & 86\\end{bmatrix} \\end{equation}`}
+</BlockMath>
 
 In Python, we can use the `dot` method or `@`:
 
@@ -469,23 +440,15 @@ Identity matrices are matrices that have the value 1 in the diagonal positions a
 
 An example:
 
-```bash
-[
-  1 0 0
-  0 1 0
-  0 0 1
-]
-```
+<BlockMath>
+  {`\\begin{equation}\\begin{bmatrix}1 & 0 & 0\\\\0 & 1 & 0\\\\0 & 0 & 1\\end{bmatrix} \\end{equation}`}
+</BlockMath>
 
 Multiplying a matrix by an identity matrix results in the same matrix. It's like multiplying by 1.
 
-```bash
-[             [             [
-  1 2 3         1 0 0         1 2 3
-  4 5 6   ·     0 1 0   =     4 5 6
-  7 8 9         0 0 1         7 8 9
-]             ]             ]
-```
+<BlockMath>
+  {`\\begin{equation}\\begin{bmatrix}1 & 2 & 3 \\\\4 & 5 & 6\\\\7 & 8 & 9\\end{bmatrix} \\cdot \\begin{bmatrix}1 & 0 & 0\\\\0 & 1 & 0\\\\0 & 0 & 1\\end{bmatrix} = \\begin{bmatrix}1 & 2 & 3 \\\\4 & 5 & 6\\\\7 & 8 & 9\\end{bmatrix} \\end{equation}`}
+</BlockMath>
 
 ### Matrix Division