I am using jupyter notebook with Python3 on windows 10. My computer has 8GB RAM and at least 4GB of my RAM is free.

But when I want to make a numpy ndArray with size 6000*6000 with this command: np.zeros((6000, 6000), dtype='float64') I got this : Unable to allocate array with shape (6000, 6000) and data type float64

I don't think this could use more then 100MB RAM. I tried to change the number to see what happens. The biggest array I can make is (5000,5000). Did I make a mistake in estimating how much RAM I need?

Jupyter notebook has a default memory limit size. You can try to increase the memory limit by following the steps:
1) Generate Config file using command:

jupyter notebook --generate-config

2) Open jupyter_notebook_config.py file situated inside 'jupyter' folder and edit the following property:

NotebookApp.max_buffer_size = your desired value

Remember to remove the '#' before the property value.
3) Save and run the jupyter notebook. It should now utilize the set memory value. Also, don't forget to run the notebook from inside the jupyter folder.

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Alternatively, you can simply run the Notebook using below command:

 jupyter notebook --NotebookApp.max_buffer_size=your_value