How can I best build a matrix like the one in the image? I can create the four databases Sector, Activities, Roles and RACI, but I do not find a way of creating a view, where Sector and Activities are shown and then for each Role we have a column, where we can add the RACI relation.

I started with the new Grid View. I have the following Relations at the moment: Sector can have multiple Activities, Roles can have multple RACI (Responsible, Accountable, Consulted, Informed).

Does anyone have an idea how I could build such a view? then publish the space as a template for all?

Such an RACI Matrix will be much more easy with the upcoming new relationship entity that the fibery team currently is working on (References Reloaded), because now we are still working with read-only lookup fields. This now means that if you create lookup fields for each RACI database item related to a user, you cannot edit the values in the table.

Here is a workaround:

Create an ‘RACI entry’, ‘Sector’, ‘Activity’ databases.
In the RACI entry database, create relation fields to Sector and Activity, plus as many multi-select fields as you have team members. The multi-select fields all have the same options (R, A, C, I)
Name=formula=entity ID, or a custom code you use for the responsibility.

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Thanks @Yuri_BC I will try this out!

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Using a Board it is possible without the need to created dedicated member fields like above, but using a ‘Responsability Assignment’ entity that has a single Activity field, single member relationship and a multi select field RACI. It allows to display more helpful fields in the assignment entity cards where needed.
Columns = member
Rows = Activity

Do you need the view to be editable?
If not, a report view will probably be the closest resemblance to the image you shared.
And it has an advantage of being easily shareable via URL