Definition
If 2 vectors are in the same \(n\)-dimensional space, then they can be added. Addition happens cooridnate-wise. In \(n\)-dimensional space, the formula is the following:
\[< a_1, a_2, \dots, a_n > + < b_1, b_2, \dots, b_n > = < a_1 + b_1, a_2 + b_2, \dots, a_n + b_n >\]
For an example in 2-dimensions:
\begin{align}
<2,3>+<4,6> & = <2+4, 3+6> \\
& = <6, 9>
\end{align}
There is no definition of a sum of 2 vectors of different dimensions.
\[<3,2> + <1,3,4> = \text{undefined}\]
Calculator
Enter 2 vectors to see their sum.
Warning: include_once(../../../snippets/math_lin_alg_keys.php): failed to open stream: No such file or directory in
/var/www/michaelbriankelly.com/digital-garden/math/bourbaki/8_vect_addition.php on line
23
Warning: include_once(): Failed opening '../../../snippets/math_lin_alg_keys.php' for inclusion (include_path='.:/usr/share/php') in
/var/www/michaelbriankelly.com/digital-garden/math/bourbaki/8_vect_addition.php on line
23
Fatal error: Uncaught Error: Call to undefined function makeKeyboard() in /var/www/michaelbriankelly.com/digital-garden/math/bourbaki/8_vect_addition.php:24
Stack trace:
#0 /var/www/michaelbriankelly.com/digital-garden/math/lesson/index.php(118): include_once()
#1 {main}
thrown in
/var/www/michaelbriankelly.com/digital-garden/math/bourbaki/8_vect_addition.php on line
24