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diff --git a/人人都能看懂的Transformer/第三章——位置编码.md b/人人都能看懂的Transformer/第三章——位置编码.md
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--- a/人人都能看懂的Transformer/第三章——位置编码.md
+++ b/人人都能看懂的Transformer/第三章——位置编码.md
@@ -172,6 +172,60 @@ tf.Tensor(
 
 
 
-### 向量加法
+### 矩阵同位置相加
+
+不管是Transformer原文中的方法还是GPT的方法，都是通过矩阵的简单相加。这里以GPT-2为例（Hugging Face开源的GPT），具体代码如下：
+
+~~~python
+import torch
+from transformers import GPT2Tokenizer, GPT2Model
+
+tokenizer = GPT2Tokenizer.from_pretrained('gpt2')  # 初始化
+model = GPT2Model.from_pretrained('gpt2')
+
+text = "LLM with me"  # 待处理的文本
+# 分词并转换为索引
+inputs = tokenizer(text, return_tensors="pt")
+input_ids = inputs["input_ids"]
+embeddings = model.get_input_embeddings()  # 获取模型的嵌入层
+input_embeddings = embeddings(input_ids)  # 将索引转换为嵌入向量
+# 获取位置编码矩阵
+position_ids = torch.arange(0, input_ids.size(1)).unsqueeze(0).to(input_ids.device)
+position_embeddings = model.wpe(position_ids)
+final_embeddings = input_embeddings + position_embeddings  # 将位置编码与词嵌入相加以获得最终的输入嵌入
+
+# 查看最终的输入嵌入
+print(final_embeddings)
+print(final_embeddings.shape)
+"""out:
+tensor([[[ 0.2321, -0.3849,  0.1550,  ...,  0.0664,  0.1922,  0.3908],
+         [ 0.0081, -0.1923,  0.1255,  ..., -0.0160,  0.1091, -0.0756],
+         [ 0.0686, -0.0744,  0.0838,  ...,  0.0598,  0.1280,  0.0136],
+         [ 0.1512, -0.0985,  0.1991,  ..., -0.1582,  0.1241,  0.0501]]],
+       grad_fn=<AddBackward0>)
+torch.Size([1, 4, 768])
+"""
+~~~
+
+<img src="../assets/image-20240427182734627.png" alt="image-20240427182734627" style="zoom:50%;" />
+
+从代码来看，embedding跟position_embeddings就是同位置元素相加。以下面的方法来检验
+
+~~~python
+print(final_embeddings[0][0][0])
+print(input_embeddings[0][0][0] + position_embeddings[0][0][0])
+"""out:
+tensor(0.2321, grad_fn=<SelectBackward0>)
+tensor(0.2321, grad_fn=<AddBackward0>)
+"""
+
+print(final_embeddings[0][1][1])
+print(input_embeddings[0][1][1] + position_embeddings[0][1][1])
+"""out:
+tensor(-0.1923, grad_fn=<SelectBackward0>)
+tensor(-0.1923, grad_fn=<AddBackward0>)
+"""
+~~~
+
+<img src="../assets/image-20240427183034655.png" alt="image-20240427183034655" style="zoom:50%;" />
 
-以GPT-2为例（Hugging Face开源的GPT），
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