diff --git a/Wiki/Math/Determinite of a Matrix.md b/Wiki/Math/Determinite of a Matrix.md deleted file mode 100644 index e69de29..0000000 diff --git a/Wiki/Math/Matricies/Determinant of a Matrix.md b/Wiki/Math/Matricies/Determinant of a Matrix.md new file mode 100644 index 0000000..a8f4586 --- /dev/null +++ b/Wiki/Math/Matricies/Determinant of a Matrix.md @@ -0,0 +1,10 @@ +For a 2 x 2 matrix: +$$ \det\begin{pmatrix} +a&b\\c&d +\end{pmatrix} = \begin{vmatrix} a&b\\c&d\end{vmatrix} = ad-bc$$ +For a 3 x 3 matrix: +$$\begin{vmatrix} a&b&c\\d&e&f\\g&h&i\end{vmatrix} = a\begin{vmatrix} e&f\\h&i\end{vmatrix} - b\begin{vmatrix} d&f\\g&i\end{vmatrix} + c\begin{vmatrix} d&e\\g&h\end{vmatrix} = a(ei-hf)-b(di-gf)+c(dh-ge)$$ +### Properties +$$\begin{matrix} +a&b\\a&b +\end{matrix}$$ \ No newline at end of file diff --git a/Wiki/Math/Vector Basics.md b/Wiki/Math/Vector Basics.md index 35a044d..4445f92 100644 --- a/Wiki/Math/Vector Basics.md +++ b/Wiki/Math/Vector Basics.md @@ -22,6 +22,8 @@ Used to find the vector of magnitude 1 in the same direction as $u$ $$a \times b = \begin{vmatrix} i&j&k\\a_1&a_2&a_3\\b_1&b_2&b_3\end{vmatrix}= i(a_2b_3-a_3b_2)-j(a_1b_3-a_3b_1)+k(a_1b_2-a_2b_1)$$ Used to create a vector that is orthogonal to both $a$ and $b$. To find what direction it will point in use the right-hand rule (thumb, pointer and middle finger). +The cross product is calculated by finding the [[Determinant of a Matrix|determinant]] of the matrix formed in the equation above with the unit vectors in the top row. + Properties: - Not commutative $$u\times v \ne v \times u$$ - Anti-commutative $$ u \times v = -(v \times u) $$