# arrow_back What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix?

8 views
What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix?

The dot product of $\mathbf{u}$  a column matrix and $\mathbf{v}$ a column matrix is:

$$\mathbf{u} \cdot \mathbf{v}=\mathbf{u}^{T} \mathbf{v}=\mathbf{v}^{T} \mathbf{u}$$

Example:

\begin{aligned} &\mathbf{u}^{T} \mathbf{v}=\left[\begin{array}{lll} 1 & -3 & 5 \end{array}\right]\left[\begin{array}{l} 5 \\ 4 \\ 0 \end{array}\right]=-7 \\ &\mathbf{v}^{T} \mathbf{u}=\left[\begin{array}{lll} 5 & 4 & 0 \end{array}\right]\left[\begin{array}{r} 1 \\ -3 \\ 5 \end{array}\right]=-7 \end{aligned}

by Platinum
(103,030 points)

## Related questions

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the dot product of u a row matrix and v a column matrix?
What is the dot product of u a row matrix and v a column matrix?What is the dot product of u a row matrix and v a column matrix? ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the dot product of u a column matrix and v a row matrix?
What is the dot product of u a column matrix and v a row matrix?What is the dot product of u a column matrix and v a row matrix? ...
close
Let $\mathbf{u}$ be a vector in $R^{100}$ whose $i$ th component is $i$, and let $\mathbf{v}$ be the vector in $R^{100}$ whose $i$ th component is $1 /(i+1)$. Find the dot product of $\mathbf{u}$ and $\mathbf{v}$.Let $\mathbf{u}$ be a vector in $R^{100}$ whose $i$ th component is $i$, and let $\mathbf{v}$ be the vector in $R^{100}$ whose $i$ th component is $1 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the dot product of u a row matrix and v a row matrix? 1 answer 3 views What is the dot product of u a row matrix and v a row matrix?What is the dot product of u a row matrix and v a row matrix? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let$a, b$and$c$be vectors in$\mathrm{R}^{3}, \times$denotes the cross product, . the dot product. Which of the following is false? 0 answers 7 views Let$a, b$and$c$be vectors in$\mathrm{R}^{3}, \times$denotes the cross product, . the dot product. Which of the following is false?Let$a, b$and$c$be vectors in$\mathrm{R}^{3}, \times$denotes the cross product, . the dot product. Which of the following is false? A.$-a \time ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is a column matrix?
Find the dot product of $u = <-5,-6,-2>$ and $v = <-3,10,8>$. Are $u$ and $v$ orthogonal?
Find the dot product of $u = <-5,-6,-2>$ and $v = <-3,10,8>$. Are $u$ and $v$ orthogonal?Find the dot product of $u = &lt;-5,-6,-2&gt;$ and $v = &lt;-3,10,8&gt;$. Are $u$ and $v$ orthogonal? ...