Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have been given a vector problem, np as I am good with vectors. But I was educated in Denmark, and I'm currently in America. The assignment is

Find $a^T\cdot b$.

Now I have never seen this $\{-\}^T$ before, what does it mean?

If it helps to explain, I have been given $a= [1,2,0]$ and $b = [2,0,4]$ and $4$ questions. Find $||a||$, Find $a^T\cdot b$, Find $a \times b$, Find $a\cdot b^T$

On a side note I, assume that $||a||$ is the length of a right?

share|improve this question
    
I think the $\cdot$ in "$\mathbf{a}^T \cdot \mathbf{b}$" is bad notation here and perhaps incorrect. $\cdot$ usually refers to the dot product. If $\mathbf{a}$ and $\mathbf{b}$ are column vectors of the same length, then $\mathbf{a}^T \mathbf{b}$ works out to be the dot product of $\mathbf{a}$ and $\mathbf{b}$ (strictly speaking, it is the 1-by-1 matrix containing whose element is that dot product). The $\cdot$ is not needed. In your problem, apparently $\mathbf{a}$ and $\mathbf{b}$ are row vectors, so $\mathbf{a}^T \mathbf{b}$ is a 3-by-3 matrix. –  Stefan Smith Nov 4 '13 at 0:38

2 Answers 2

up vote 0 down vote accepted

They are considered as matrices, usually column vectors, and $^T$ means transpose, i.e. exchanging the rows and columns (exchanging the indices: $(a_{ij})^T:=(a_{ji})$.) So, $a^Tb$ is the scalar product $\langle a,b\rangle$, and $ab^T$ will be a (rank 1) matrix of size $3\times 3$.

share|improve this answer
1  
If $a$ and $b$ are row vectors, then you have the inner and outer products the wrong way around. –  Daryl Sep 30 '12 at 23:14
    
So the correct answer to a^Tb will be [2] right? –  DoomStone Sep 30 '12 at 23:32
    
@DoomStone Is the original $a$ equal to $[1,2,0]$? If so, then $ab^T$ is $2$. But if the original $a$ is $\begin{bmatrix}1\\2\\0\end{bmatrix}$ (as is more common with North American mathematicians) then $a^Tb$ is $2$. –  alex.jordan Oct 1 '12 at 0:35
    
you are right.. –  Berci Oct 1 '12 at 11:31

It could be that the $T$ indicates the transpose. If both $a$ and $b$ are row vectors as you have written them, then you will have to take transposes in order to multiply them.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.