寻求入门级线性代数在线学习资源（偏好网站/在线PDF，明确学习进度）

Hey John, based on your current linear algebra background, here are some solid entry-level resources tailored to help you dive into row spaces, column spaces, and related topics smoothly:

• MIT OpenCourseWare Linear Algebra：This course fits your stage perfectly. You can jump straight to lectures around Lesson 10, which focus on subspaces like row space, column space, and null space. The content builds directly on the basics you’ve mastered—bases, linear independence, and matrices as transformations—so you won’t feel disconnected. Each lecture comes with supporting notes and problem sets to reinforce your learning.
• Khan Academy Linear Algebra Module：Head to the "Subspaces and the basis for a subspace" section, which transitions seamlessly into row and column spaces. The visual explanations here are excellent for grasping the geometric intuition behind these spaces, and interactive quizzes let you test your understanding step-by-step, building on your existing knowledge of vector spaces and dimension.

• Gilbert Strang’s Introduction to Linear Algebra (PDF version)：Chapters 3 and 4 are exactly what you need. Chapter 3 links matrices as linear transformations to column space concepts, while Chapter 4 dives into row space, null space, and the rank-nullity theorem—all tied back to the dimension invariant you already understand. The examples are practical, and the explanations are written in a conversational, easy-to-follow style.
• University of Berkeley Introductory Linear Algebra Lecture Notes (PDF)：These notes include a dedicated section that starts with a quick recap of subspaces and bases, then moves into row and column spaces. They break down how these spaces connect to matrix rank and use the dimension concept you know to explain why key properties hold. The exercises are targeted to help you apply new ideas without feeling overwhelmed.

I’ve recommended these resources to peers at your exact learning stage before, and they’ve found them really helpful for bridging the gap between what you already know and the new topics you’re about to tackle.

内容的提问来源于stack exchange，提问作者John