Add PyTorch .sgn() tensor operation documentation

content/pytorch/concepts/tensor-operations/terms/sgn/sgn.md

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+---
+Title: '.sgn()'
+Description: 'Computes the sign of each element in the input tensor, returning a tensor with the same shape.'
+Subjects:
+  - 'Computer Science'
+  - 'Data Science'
+Tags:
+  - 'Deep Learning'
+  - 'Methods'
+  - 'PyTorch'
+  - 'Tensor'
+CatalogContent:
+  - 'intro-to-py-torch-and-neural-networks'
+  - 'paths/data-science'
+---
+
+The **`.sgn()`** function computes the sign of each element in the input [tensor](https://www.codecademy.com/resources/docs/pytorch/tensors), applied element-wise. For real-valued tensors, it returns -1 for negative values, 0 for zero, and 1 for positive values. For complex-valued tensors, it returns the complex sign (the tensor divided by its absolute value), which gives the unit vector in the direction of each complex number.
+
+## Syntax
+
+```pseudo
+torch.sgn(input, *, out=None) → Tensor
+```
+
+**Parameters:**
+
+- `input` (Tensor): The input tensor (can be real or complex).
+- `out` (Tensor, optional): Optional output tensor to store the result.
+
+**Return value:**
+
+A tensor with the same shape as `input`, containing the sign of each element.
+
+## Example 1: Using `.sgn()` with a Real-Valued Tensor
+
+In this example, `.sgn()` computes the sign of each element in a real-valued tensor:
+
+```py
+import torch
+
+# Create a tensor with positive, negative, and zero values
+x = torch.tensor([-5.0, -2.5, 0.0, 2.5, 5.0])
+
+# Compute the sign
+result = torch.sgn(x)
+
+print(result)
+```
+
+The output of this code is:
+
+```shell
+tensor([-1., -1.,  0.,  1.,  1.])
+```
+
+## Example 2: Applying `.sgn()` element-wise to a 2D tensor
+
+In this example, `.sgn()` is applied to a 2D tensor:
+
+```py
+import torch
+
+# Create a 2x3 tensor
+matrix = torch.tensor([[-3.0, -1.0, 0.0], [1.0, 2.0, 3.0]])
+
+# Compute the sign
+result = torch.sgn(matrix)
+
+print(result)
+```
+
+The output of this code is:
+
+```shell
+tensor([[-1., -1.,  0.],
+        [ 1.,  1.,  1.]])
+```
+
+## Example 3: Using `.sgn()` with Complex Numbers
+
+For complex-valued tensors, `.sgn()` returns the complex sign, which is the unit vector in the direction of each complex number (computed as `x / |x|`):
+
+```py
+import torch
+
+# Create a tensor with complex numbers
+z = torch.tensor([1+2j, -1+2j, 3-4j])
+
+# Compute the complex sign
+result = torch.sgn(z)
+
+print(result)
+```
+
+The output of this code is:
+
+```shell
+tensor([0.4472+0.8944j, -0.4472+0.8944j, 0.6000-0.8000j])
+```
+
+In this example, each result has a magnitude of 1 (a unit vector), pointing in the direction of the original complex number.