Question: Are both University of California, Los Angeles, and Princeton University private Ivy League research universities?
Context: The 2016–17 Princeton Tigers men's basketball team represented Princeton University during the 2016–17 NCAA Division I men's basketball season.  The Tigers, led by sixth-year head coach Mitch Henderson, played their home games at Jadwin Gymnasium as members of the Ivy League.  They finished the season 23–7, 14–0 in Ivy League play to win the Ivy League regular season championship.  They defeated Penn and Yale to win the inaugural Ivy League Tournament championship.  As a result, they earned the conference's automatic bid to the NCAA Tournament where they lost in the First Round to Notre Dame. This list of Ivy League medical schools outlines the seven universities of the Ivy League that host a medical school.  Only one Ivy League university, Princeton University, does not have a medical school.  All Ivy League medical schools are located in the Northeast region of the United States and are privately owned and controlled.  Only two of the schools, at Dartmouth and Penn, are located adjacent to the undergraduate campuses.  The schools at Brown, Columbia, Harvard, and Yale, are located on separate campuses in the same metropolitan area as the university.  The school at Cornell, Weill Cornell Medicine, is located in New York City, far from the main Ithaca campus. The 2016 Princeton Tigers football team represented Princeton University in the 2016 NCAA Division I FCS football season.  They were led by seventh year head coach Bob Surace and played their home games at Princeton University Stadium.  Princeton is a member of the Ivy League.  They finished the season 8–2, 6–1 in Ivy League play to finish in a tie with Penn for the Ivy League title, their first since 2013. The Cornell–Princeton lacrosse rivalry is a college lacrosse rivalry between Princeton University and Cornell University and their respective men's lacrosse teams, Princeton Tigers and Cornell Big Red.  The rivalry stems from the dominance of the two programs in the Ivy League where in the first 61 seasons (including the 2016 season) Cornell has won 29 Ivy League Championships (18 outright, 11 shared) and Princeton has won 27 league titles (18 outright, 9 shared).  The next nearest team is Brown with ten titles (five outright, five shared) CornellBigRed.com describes the rivalry as "The marquee matchup in Ivy League lacrosse".  Cornell claims three NCAA Division I Men's Lacrosse Championships (1971, 1976, 1977) and four pre-NCAA era national championships (1903, 1907, 1914, 1916).  Princeton claims six NCAA championships (1992, 1994, 1996, 1997, 1998, 2001) and six pre-NCAA era national championships (1884, 1885, 1937, 1942, 1951, 1953).  Princeton last won the Ivy League in 2012 while Cornell won the title in 2013 and 2014. The University of California, Los Angeles (UCLA) is a public research university in the Westwood district of Los Angeles, California, United States.  It became the Southern Branch of the University of California in 1919, making it the second-oldest undergraduate campus of the ten-campus University of California system.  It offers 337 undergraduate and graduate degree programs in a wide range of disciplines.  UCLA enrolls about 31,000 undergraduate and 13,000 graduate students, and had 119,000 applicants for Fall 2016, including transfer applicants, the most applicants for any American university. The 2012 Princeton Tigers football team represented Princeton University in the 2012 NCAA Division I FCS football season.  They were led by third year head coach Bob Surace and played their home games at Princeton University Stadium.  They are a member of the Ivy League.  They finished the season 5–5, 4–3 in Ivy League play to finish in a three way tie for third place.  Captain Mike Catapano was Ivy League Defensive Player of the Year.  He was drafted in the 2013 NFL Draft by the Kansas City Chiefs with the first pick of the seventh round (207th overall) becoming Princeton's first draftee since Dennis Norman in the 2001 NFL Draft. The 1966–67 Princeton Tigers men's basketball team represented Princeton University in intercollegiate college basketball during the 1966–67 NCAA University Division men's basketball season.  Butch van Breda Kolff served as head coach and the team captain was Ed Hummer.  The team played its home games in the Dillon Gymnasium on the University campus in Princeton, New Jersey.  The team was the champion of the Ivy League, which earned them an invitation to the 23-team 1967 NCAA Men's Division I Basketball Tournament.  This was van Breda Kolff's final year as head coach at Princeton.  Upon his retirement to go coach the Los Angeles Lakers, he eclipsed R. B. Smith's fifty-eight-year-old Ivy League winning percentage record with a 76.9% mark (103–31).  The record stood until Bill Carmody stepped down in 2000.  His team's helped Princeton end the decade with a 72.6 winning percentage (188–71), which was the tenth best in the nation. Princeton University is a private Ivy League research university in Princeton, New Jersey, United States.  Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution.  The institution moved to Newark in 1747, then to the current site nine years later, where it was renamed Princeton University in 1896. The 2014 Princeton Tigers football team represented Princeton University in the 2014 NCAA Division I FCS football season.  They were led by fifth-year head coach Bob Surace and played their home games at Princeton University Stadium.  Princeton were a member of the Ivy League.  They finished the season 5–5, 4–3 in Ivy League play to finish in fourth place. The 2012–13 Princeton Tigers men's basketball team represented Princeton University during the 2012–13 NCAA Division I men's basketball season.  The Tigers, led by second year head coach Mitch Henderson, played their home games at Jadwin Gymnasium and were members of the Ivy League.  The Tigers entered the season as the favorites to win the Ivy League regular season title.  For the first time in school history, the team was served by a quartet of captains.  They finished the season 17–11, 10–4 in Ivy League play to finish in second place.  They chose not to participate in a postseason tournament.  Following the season Hummer earned Ivy League Men's Basketball Player of the Year.
Answer: no