How can I connect my mini- ipad to a monitor with a female DVI connector in the back?

For iPad mini you'd need a lightning adapter. The lightning adapter has a HDMI port. Then plug a HDMI to DVI adapter into that to go to the DVI connection on the monitor.

Questions & Answers: StarTech.com MDP2DVI Mini DisplayPort to DVI Adapter - 1920x1200 - 1080p - Monitor Adapter - Mini DisplayPort Adapter - Mini DP to DVI

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StarTech.com MDP2DVI Mini DisplayPort to DVI Adapter - 1920x1200 - 1080p - Monitor Adapter - Mini DisplayPort Adapter - Mini DP to DVI

Connect a DVI display to a Mini DisplayPort equipped PC or MAC
Compatible with any Surface Pro or Lenovo ThinkPad X1 Carbon laptops that are equipped with mDP
Passive Single Link / DP++ / Dual-mode DisplayPort
Support Resolutions up to 1920x1200
Thunderbolt to DVI Compatible
Connects to your Laptop Thunderbolt port
MDP to DVI Adapter / Mini Display Port to DVI Adapter / Mini DP to DVI / Comparable to 0B47090 / Thunderbolt to DVI Converter

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