What makes a company innovative?

Given my experience with startups and corporations on Open Innovation programs, I would say that a company is innovative when it successfully launches either a product or a service that addresses a problem in such a way that was never seen before and that ultimately disrupts the market; it teaches consumers a new way to solve a problem. This is Uber, enabling users to ask for drivers through a smartphone and then rate them; or Amazon, enabling people to purchase any product always from the same store - at a distance of a click. Innovative companies introduce a new method that people learn and adopt at scale – since it solves their problem quicker, faster, cheaper.
To design such an innovative company, I would focus on forming a dream team: a diverse group of different nationalities and backgrounds - including exact scientists and social scientists with different professional experiences. An innovative company needs dreamers – the ones who seek the unimaginable - what everyone sees as impossible; the ones who scratch the impossible and believe it will happen. But innovative companies also need doers - those who look at the dreamers' plan and make it happen no matter what; the ones who are driven by results and find the ways to keep the company running and profitable. Both profiles are needed, and they have to work together - sometimes disagreeing; sometimes leading the company into the future.
Transforming an established company to become more innovative is tougher though. In this case, companies need a ‘Kamikaze’ team – an external team that reports to the head of each department. The mission of this special team is to identify bottlenecks in internal processes, spot those highly motivated individuals inside the corporation, understand the current status quo and capture feedback on improvements; to spot problems with current clients, benchmark with competitors, and gather insights about other aspects of the company that may be crucial for understanding how it is being run, what works and what does not [ … ]