The advent of online learning platforms has revolutionized the way we approach education, particularly in mathematically heavy disciplines. One such area is Linear Algebra, a branch of mathematics focusing on vector spaces and the linear transformations between them. For students grappling with these abstract concepts, an online linear algebra tutor can be an invaluable asset. However, before engaging one, it's crucial to understand some essential facets. Here are ten points that I wish I'd comprehended sooner.

• Expertise and Qualifications:
  Online tutors, like their traditional counterparts, come with a range of qualifications and expertise. A tutor may hold a PhD in Mathematics, while another might be an undergraduate student with a knack for explaining complex concepts in simple terms. It's crucial to ascertain the tutor's credentials and, more importantly, their ability to impart knowledge effectively.

• Teaching Methodology:
  Linear Algebra, with its vector spaces, matrices, and eigenvalues, can be daunting. The teaching methodology employed by the tutor can significantly impact a student's understanding. Some tutors may use an abstract, proof-based approach while others might prefer a more practical, application-based method. Identifying which approach suits you best can save you from future frustration.

• Availability and Flexibility:
  Unlike traditional tutoring, online sessions offer greater flexibility. However, tutors will always have their schedules. Before signing up, ensure the tutor's availability matches your learning rhythm. If you're a night owl or on the other side of the globe, confirm whether your tutor can accommodate your timing preferences.

• Use of Technology:
  Online tutoring inherently relies on technology, but the specific tools used can vary greatly. Some tutors might use interactive whiteboards, while others might limit themselves to video calls. Familiarity with these tools can enhance the learning experience, so it's worth exploring the technologies employed by the tutor and whether they align with your comfort level.

• Pedagogical Resources:
  Does the tutor provide supplementary materials like practice problems, reading lists, or software tutorials? These resources can augment your understanding of linear algebra, providing a more holistic learning experience.

• Progress Tracking:
  A competent tutor should be able to track your progress and adapt the teaching strategy accordingly. Whether it's through regular quizzes, assignments, or simply observing your problem-solving process, progress tracking is key to a successful tutoring engagement.

• Cost:
  While it is important to invest in quality education, understanding the cost implications before hiring a tutor can prevent unwelcome surprises. The price depends on the tutor's qualifications, the length and frequency of sessions, and other value-added services.

• Communication Style:
  An often overlooked aspect is the tutor's communication style. Does the tutor encourage questions? Are they patient and understanding? A tutor’s ability to create a comfortable learning environment is just as important as their mathematical prowess.

• Reviews and Reputation:
  With numerous online platforms hosting tutor profiles, it's easier than ever to gauge a tutor's effectiveness through reviews and ratings. Previous students' experiences can offer valuable insights into the tutor's teaching style, punctuality, and overall approachability.

• Trial Sessions:
  Many online tutors offer free or discounted trial sessions. These can be an excellent opportunity to evaluate whether the tutor's teaching style, availability, and communication skills align with your expectations.

In summary, an online linear algebra tutor can provide personalized, convenient, and engaging learning experiences. However, it's essential to consider the factors above before embarking on this educational journey. As with any investment, due diligence can ensure that you reap the maximum benefits. After all, Linear Algebra constitutes the backbone of many modern scientific disciplines, making a deep understanding of its tenets well worth the effort.

Remember, the ideal tutor doesn't just teach linear algebra. They inspire an appreciation for the beauty and intricacy of the mathematical world and equip you with the tools to explore it independently.