2026考研数学备考:向量的内积与正交化

小文老师
考研数学2026考研初试时间预计在12月底,对于基础不扎实的同学来说,现在还有时间进行提升,文都老师提炼核心考查点,多维度剖析考纲要求,核心要点反复持续输出强化记忆,科学备考更高效。本文整理2026考研数学备考:向量的内积与正交化,快来一起学习一下~,快来一起学习一下~

向量的内积与正交化

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




今天的2026考研数学备考:向量的内积与正交化,快来一起学习一下~ 你都记住了么?接下来的考研数学备考小可爱们可以每天有计划地背诵哦~


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