No. Unix pre-dates Linux by a lot. Unix was basically one of the very first operating systems, from the earliest days of computing. Along with a few other early and often related operating systems, most notably BSD, they set the industry standard for what operating systems are and how they work. A large part of that became the formal standard called POSIX. And today, the vast majority of all operating systems in existence follow that standard (or nearly so), that includes Mac OSX, Linux, Solaris, QNX, several BSD derivatives, Android, and a number of specialized operating systems (if they're not using Linux).
In fact, Linus Torvalds explained many times that he basically created Linux because he had worked with and studied Unix systems and thought they were awesome and wanted one for his personal computer, but couldn't afford it (a license for such an early industrial-grade OS is expensive, only companies and institutions could afford it). So, he basically wrote an OS from scratch that could act as a drop-in replacement for Unix, and so it is. By all accounts, Linux is an alternative (and open-source) implementation of Unix. And now, Linux is by far more wide-spread than Unix, making it the lead figure or most visible representative of this Unix family of operating systems.
Today, all of the systems that follow this Unix / POSIX standard are collectively referred to as "Unix-like" systems, because from the perspective of writing applications, programs and scripts, they all look nearly identical to a Unix system. Of course, there are differences between them, but it's mostly in the form of additional features (that you don't have to use), or invisible differences (such as in the way the kernel works, which, as an application developer or a user, you will never see unless you dig really deep into it).
Really, the only notable exception is Windows (and DOS before it), it's the black sheep of operating systems, the only one that isn't Unix-like (but you can make it Unix-like through something like Cygwin). Sadly, Windows (still) holds the biggest portion of the home users' market (but, fortunately, not in many other markets).
Linux is NOT Unix, though they share a lot of design features, and support many of the same tools and application sets, though each application needs to be built for Unix or Linux separately.
Unix was developed by Brian Kernighan, Dennis Ritchie, and Ken Ken Thompson at AT&T Bell Labs in the 1970's. They needed a "free" version of the Multics time-sharing computer OS, so they invented their own! The rest, as they say, is history.
Linus Torvalds was working with Minix, written as a university teaching project by Andrew Tannenbaum in the mid-1980's as an example how to build a Unix-like system. After awhile, Linus decided to write his own kernel, and Linux was born. Both Unix and Minix were inspirations to him, and he built upon their work.
FWIW, Kernighan and Ritchie invented the C language, and used it to implement Unix (with some machine-specific assembly language, I'm sure).
The story of Linux is contained within a single video, where on top of what rubben said, long story short, Linus had created the kernel in his spare time and a multiple individuals have developed "GNU's not unix" (GNU),lead by Richard Stallman, when those two were combined, Linux was born
Unix is an old "program", something like DOS. It's like a parent of Linux and iOS. They're both UNIX based. If you would look at this biologically, Unix in Neanderthal and Linux/iOS have evolved further and are better (in my opinion).
As stated above, Linux is a clone of Unix, but there are differences between these two operating systems. The major differences are:
Linux – most Linux distributions are free
Unix - most UNIX like operating systems are not free Usage
Linux - mobile phones, tablet computers, desktop computers
Unix - developed mainly for mainframes and servers Source model
Linux - open source
Unix - mostly closed source Examples
Linux - Ubuntu, Debian, Red Hat, openSUSE
Unix - OS X, Solaris, IBM AIX Manufacturer
Linux - Linux kernel is developed by the community.
Unix – IBM, HP, Oracle