# Orthogonal vector/matrix

#### Petrus

##### Well-known member
Hello MHB,
I wounder if I did understand correct, If we got 3 vector and they all are orthogonala, $$\displaystyle v_1=(x_1,y_1,z_1)$$,$$\displaystyle v_2=(x_2,y_2,z_2)$$,$$\displaystyle v_3=(x_3,y_3,z_3)$$ does that also mean that the matrix orthogonal so the invrese for the matrix is transport?

Regards,
$$\displaystyle |\pi\rangle$$

#### Ackbach

##### Indicium Physicus
Staff member
Close, but not quite. A matrix being orthogonal means that its columns are orthonormal.

#### Petrus

##### Well-known member
Close, but not quite. A matrix being orthogonal means that its columns are orthonormal.
How can I check if a columns are orthonormal? If I got it correct if $$\displaystyle v_1,v_2,v_3$$ shall be orthonormal that means that $$\displaystyle v_1*v_2*v_3=0$$

Regards,
$$\displaystyle |\pi\rangle$$

#### Ackbach

##### Indicium Physicus
Staff member
Check that $v_{i} \cdot v_{j}=\delta_{ij}$. Here
$$\delta_{ij}=\begin{cases}0,\quad &i \not=j \\ 1,\quad &i=j \end{cases}$$
is the Kronecker delta.