Answers.Body: <p>The notation <span class="math-container">$W_{k, \cdot}$</span> likely refers to the <span class="math-container">$k$</span>-th row of <span class="math-container">$W$</span>. The dot just suggests taking all the elements in the row. It is just a convenient way to index an entire row of a matrix.</p>
  <p>Similar usage of this indexing notation appears in 'Linear Algebra Done Right' (3rd edition) by Sheldon Axler in section 3.44.</p>
  
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Body: <p>In his article <a href="https://arxiv.org/abs/1411.2738" rel="nofollow noreferrer">word2vec Parameter Learning Explained</a> Xin Rong uses the dot notation as an index for matrix (at the second page in the first formula).</p>
  <p><span class="math-container">$$ h = W^{T}x = W^{T}_{(k,\cdot)} := {v^{T}}_{w_I} \tag 1$$</span></p>
  <p>If I understand the notation correctly, it means summarizing all the elements.</p>
  <p>Am I correct in thinking that in this case this is just a formalism in the notation since as it stated in the paper:</p>
  <p><span class="math-container">$$ x_k=1 \ \text{and} \ x_{k'}=0 \ \text{for} \ k' \neq k $$</span></p>
  <p>all other elements will be zero and no summation is necessary?</p>
  <p>Is this just a notation to keep operations on matrices and vector consistent or I am missing something important?</p>
  <p>I found similar question in the <a href="https://math.stackexchange.com/questions/2918934/what-does-a-dot-mean-in-matrix-element-index">What does a dot mean in matrix element index?</a>, but the answer seems to be specific for that case and the link they provide in comments doesn't open. So, in case somebody could refer to book/textbook with introducing this notation, please help.</p>
  
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Comments.Text: The notation $W_{k, \cdot}$ likely refers to the $k$-th row. The dot just suggests taking all the elements in the row. It is just a convenient way to index an entire row of a matrix.
Comments.UserDisplayName: hff1
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Comments.Text: @hff1, thank you, makes sense for this formula, although as I understand it contradicts to the [What does a dot mean in matrix element index?](https://math.stackexchange.com/questions/2918934/what-does-a-dot-mean-in-matrix-element-index) (updated the question). Is there any source like a book or a textbook where this is introduced in math?
Comments.UserDisplayName: Damir Tenishev
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Comments.Text: I know it appears in 'Linear Algebra Done Right' (3rd edition) by Sheldon Axler in one of the sections where he introduces matrices. You can also see it as 'numpy-like' notation: compare with ```W[k, :]``` for example
Comments.UserDisplayName: hff1
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Comments.Text: @hff1, thank you so much! Found in the book in the section `3.44 Notation ...`. Still not sure what are the roots of this notation (namely, when it comes from), but this answers the question just fine. If you like, post your comment as the answer so that I could accept it to make this beneficial for future readers.
Comments.UserDisplayName: Damir Tenishev
Tags: <word-embedding><embeddings><word2vec><cbow>
Title: Dot notation for matrix element index in formula of word2vec embedding calculation
UserDisplayName: Damir Tenishev
ThreadText: # Dot notation for matrix element index in formula of word2vec embedding calculation
  
  (Asked by: username_0 on 2024-06-08)
  
  In his article [word2vec Parameter Learning Explained](https://arxiv.org/abs/1411.2738) Xin Rong uses the dot notation as an index for matrix (at the second page in the first formula).
  
  $$ h = W^{T}x = W^{T}\_{(k,\cdot)} := {v^{T}}\_{w\_I} \tag 1$$
  
  If I understand the notation correctly, it means summarizing all the elements.
  
  Am I correct in thinking that in this case this is just a formalism in the notation since as it stated in the paper:
  
  $$ x\_k=1 \ \text{and} \ x\_{k'}=0 \ \text{for} \ k' \neq k $$
  
  all other elements will be zero and no summation is necessary?
  
  Is this just a notation to keep operations on matrices and vector consistent or I am missing something important?
  
  I found similar question in the [What does a dot mean in matrix element index?](https://math.stackexchange.com/questions/2918934/what-does-a-dot-mean-in-matrix-element-index), but the answer seems to be specific for that case and the link they provide in comments doesn't open. So, in case somebody could refer to book/textbook with introducing this notation, please help.
  
  **Tags:** word-embedding, embeddings, word2vec, cbow
  > **Comments:**
  > **username_1**: The notation $W_{k, \cdot}$ likely refers to the $k$-th row. The dot just suggests taking all the elements in the row. It is just a convenient way to index an entire row of a matrix.  
  > **username_0**: @hff1, thank you, makes sense for this formula, although as I understand it contradicts to the [What does a dot mean in matrix element index?](https://math.stackexchange.com/questions/2918934/what-does-a-dot-mean-in-matrix-element-index) (updated the question). Is there any source like a book or a textbook where this is introduced in math?  
  > **username_1**: I know it appears in 'Linear Algebra Done Right' (3rd edition) by Sheldon Axler in one of the sections where he introduces matrices. You can also see it as 'numpy-like' notation: compare with ```W[k, :]``` for example  
  > **username_0**: @hff1, thank you so much! Found in the book in the section `3.44 Notation ...`. Still not sure what are the roots of this notation (namely, when it comes from), but this answers the question just fine. If you like, post your comment as the answer so that I could accept it to make this beneficial for future readers.  
  
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  ## 1 answers
  
  ### Answer by username_1 on 2024-06-09. Score: 1 | Accepted answer
  
  The notation $W\_{k, \cdot}$ likely refers to the $k$-th row of $W$. The dot just suggests taking all the elements in the row. It is just a convenient way to index an entire row of a matrix.
  
  Similar usage of this indexing notation appears in 'Linear Algebra Done Right' (3rd edition) by Sheldon Axler in section 3.44.
  
  
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