Does any way exist to prove or disprove that the projections of two linearly independent vectors on plane are also linearly independent (or not?)
2026-03-26 19:19:08.1774552748
Are projections of linear independent vector on a plane also linearly independent
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As @User20354 said in general there is no guarantee that they ramins independent.
Suppose you want to project your vectors to a subspace. At first consider a basis for that subspace and then extend it to whole vector space. Now suppose your vectors presentations on this basis. When you project your vectors to that subspace, in fact, you only keep the term that belong to subspace basis and throw other terms out. So if they are independent in these left terms, they remain independent. For two vectors it easy to check that these coefficient in multiple of each other or not.