Atari, the nation's largest personal-computer and video games company, will make its computer software available for competing brands of personal computers this summer, the company announced yesterday. These include Apple Computer Inc., Commodore International, Tandy Corp. and Texas Instruments Inc.

This means the Warner Communications Inc. subsidiary would make both its home management and educational programs compatible with such machines as Commodore's 64 and VIC-20 computers and Radio Shack's Color Computers. Home computer versions of Atari's popular video games such as Pac-Man and Space Invaders also would be available.

"Atari is very committed to the concept that software will play an increasing role in the personal computer market," said Atari spokesman Bruce Entin. "There are a lot of computers out there and they aren't all Atari's."

Industry analysts estimate that more than 2.5 million personal computers were sold last year, with close to double those sales predicted for this year. Atari had less than 20 percent of those sales. Moreover, the lines between video game console and personal computer keyboard are blurring. Atari will introduce a computer keyboard for its low-cost video games unit this summer.

Despite the wide diversity of hardware and price wars between computer companies seeking market share, most personal-computer watchers say that software will be the key to profits. Future Computing, a research firm in Texas, estimates that the personal computer software market to be worth more than $5 billion by 1985.

Atari's home computer division, which produces the machines, has not been a major money maker for the company. The bulk of Atari's $2.05 billion in 1982 revenues came from its arcade and home video game operations.