https://binarydog.top/tags/linearalgebra/ Recent content in LinearAlgebra on PseudorandomDog's Blog Hugo zh-CN Thu, 16 Apr 2026 00:00:00 +0000 https://binarydog.top/posts/two-perspectives-of-why-column-rank-equals-row-rank-and-their-connections/ Thu, 16 Apr 2026 00:00:00 +0000 https://binarydog.top/posts/two-perspectives-of-why-column-rank-equals-row-rank-and-their-connections/ <p>Frankly speaking, there&rsquo;s no need to write a blog explaining this corollary since it has been taught on undergraduate classes for decades. But when I was reviewing my Algebra book, I found myself pondering a deeper question: what is the <strong>intrinsic</strong> connection between these two perspectives? At least I need an explanation other than Mathematic proof.</p> <h2 class="heading" id="review-fundamental-theorem-of-linear-maps"> Review: Fundamental Theorem of Linear Maps <a class="anchor" href="#review-fundamental-theorem-of-linear-maps">#</a> </h2> <p>Matrices are essentially representations of linear maps. I&rsquo;ll begin by recalling the fundamental theorem of linear maps.</p>