From 8d160e3ee4edfd255190c7cbd0e6b618751b03cc Mon Sep 17 00:00:00 2001 From: songyc macbook Date: Sat, 18 Jul 2026 21:52:12 +0900 Subject: [PATCH] =?UTF-8?q?1=EC=9E=A5=20=EC=A0=95=EB=A6=AC:=20=EC=82=AC?= =?UTF-8?q?=EC=9A=A9=EC=9E=90=20=ED=95=98=EC=9D=B4=EB=9D=BC=EC=9D=B4?= =?UTF-8?q?=ED=8A=B8=2011=EA=B0=9C=20=EC=B0=B8=EC=A1=B0=20=EC=97=B0?= =?UTF-8?q?=EA=B2=B0,=20=EC=9E=91=EC=97=85=20=ED=9D=90=EB=A6=84=20?= =?UTF-8?q?=EA=B7=9C=EC=B9=99=20=ED=99=95=EC=A0=95?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - 영역 하이라이트 uuid를 정리 본문 해당 위치에 📌 블록 참조로 삽입 - CLAUDE.md 작업 흐름을 6단계 사이클(선행 학습 → 1차 하이라이트 → 정리 → 추가 제안 → 2차 하이라이트·다듬기 → 카드화)로 갱신 - 하이라이트 영역 이미지 등 Logseq 생성 파일 등록 Co-Authored-By: Claude Fable 5 --- CLAUDE.md | 18 ++- assets/1장_벡터와_행렬_1784335993046_0.edn | 134 +++++++++++++++++- ...0f-8720-4ae8-b8d5-2399b6c6cb65_1784378637852.png | Bin 0 -> 73508 bytes ...14-9a2e-4601-ab79-a26e887561a0_1784378643210.png | Bin 0 -> 46685 bytes ...2c-fe72-4e43-b869-f6d77622c379_1784378667056.png | Bin 0 -> 57732 bytes ...38-a296-44b4-9477-21b6393c05ce_1784378677540.png | Bin 0 -> 80465 bytes ...53-d1c5-49ea-b1e1-e9b008137458_1784378705862.png | Bin 0 -> 52342 bytes ...74-72d1-4ac2-bb64-3f37b95a3f5e_1784378738809.png | Bin 0 -> 149106 bytes ...79-424b-4e07-9595-4adb2c4014fa_1784378743733.png | Bin 0 -> 154111 bytes ...dd-cab9-4dcd-92c2-1cbaf5c9fc6c_1784378586870.png | Bin 0 -> 289634 bytes ...91-28ea-4a27-896d-360fd2f1725b_1784378767689.png | Bin 0 -> 153172 bytes ...a0-8bcd-4080-b864-6cefab1bb900_1784378783139.png | Bin 0 -> 159600 bytes ...f6-a99c-4df9-857c-944875fdbec4_1784378612799.png | Bin 0 -> 218962 bytes pages/1장 벡터와 행렬.md | 11 ++ pages/hls__1장_벡터와_행렬_1784335993046_0.md | 78 ++++++++++ 15 files changed, 234 insertions(+), 7 deletions(-) create mode 100755 assets/1장_벡터와_행렬_1784335993046_0/13_6a5b750f-8720-4ae8-b8d5-2399b6c6cb65_1784378637852.png create mode 100755 assets/1장_벡터와_행렬_1784335993046_0/13_6a5b7514-9a2e-4601-ab79-a26e887561a0_1784378643210.png create mode 100755 assets/1장_벡터와_행렬_1784335993046_0/17_6a5b752c-fe72-4e43-b869-f6d77622c379_1784378667056.png create mode 100755 assets/1장_벡터와_행렬_1784335993046_0/18_6a5b7538-a296-44b4-9477-21b6393c05ce_1784378677540.png create mode 100755 assets/1장_벡터와_행렬_1784335993046_0/28_6a5b7553-d1c5-49ea-b1e1-e9b008137458_1784378705862.png create mode 100755 assets/1장_벡터와_행렬_1784335993046_0/30_6a5b7574-72d1-4ac2-bb64-3f37b95a3f5e_1784378738809.png create mode 100755 assets/1장_벡터와_행렬_1784335993046_0/30_6a5b7579-424b-4e07-9595-4adb2c4014fa_1784378743733.png create mode 100755 assets/1장_벡터와_행렬_1784335993046_0/3_6a5b74dd-cab9-4dcd-92c2-1cbaf5c9fc6c_1784378586870.png create mode 100755 assets/1장_벡터와_행렬_1784335993046_0/42_6a5b7591-28ea-4a27-896d-360fd2f1725b_1784378767689.png create mode 100755 assets/1장_벡터와_행렬_1784335993046_0/45_6a5b75a0-8bcd-4080-b864-6cefab1bb900_1784378783139.png create mode 100755 assets/1장_벡터와_행렬_1784335993046_0/5_6a5b74f6-a99c-4df9-857c-944875fdbec4_1784378612799.png diff --git a/CLAUDE.md b/CLAUDE.md index 7da2d1b..157ebfd 100755 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -4,9 +4,14 @@ ## 작업 흐름 (중요) -1. 사용자가 먼저 학습한다 (PDF 등 원자료 기준). -2. Claude가 내용을 정리해 페이지에 작성한다. -3. 사용자가 그 정리를 바탕으로 직접 다듬고 **Anki 카드는 사용자가 직접 만든다**. +한 단원을 다음 사이클로 정리한다: + +1. **사용자 선행 학습** — 사용자가 그 단원을 먼저 혼자 공부한다 (PDF 원자료 기준). +2. **사용자 1차 하이라이트** — 공부한 내용을 바탕으로 사용자가 Logseq에서 그 단원 PDF에 하이라이트한다. +3. **Claude 정리** — 책 내용과 사용자의 하이라이트를 바탕으로 단원 페이지에 정리를 작성한다. 사용자가 만든 하이라이트는 `((uuid))` 블록 참조로 정리 본문의 해당 위치에 포함한다 (아래 「PDF 하이라이트·이미지 활용」 참고). +4. **추가 하이라이트 제안** — 정리하면서 Claude 판단에 원문 링크가 더 필요한 부분이 있으면, 정리 완료 보고에 **하이라이트 요청 목록**(쪽 번호 + 부분)을 담아 제안한다. +5. **사용자 2차 하이라이트 → Claude 다듬기** — 사용자가 제안을 (자기 판단으로 취사선택하여) 하이라이트하고 알려주면, Claude가 hls 페이지에서 새 uuid를 읽어 참조를 채워 정리를 다듬는다. +6. **사용자 마무리** — 사용자가 직접 Anki 카드화하고 자기 방식으로 세부 수정하여 그 단원 정리를 마무리한다. → 따라서 Claude는 **카드 문법(`#card`, `{{cloze ...}}`, `{{c1 ...}}`, `extra::`, `#+BEGIN_EXTRA`)을 새로 추가하지 않는다.** 일반 정리 텍스트만 작성한다. 기존에 있는 카드 문법과 `id::` 속성은 절대 수정·삭제·복제하지 않는다. @@ -72,10 +77,11 @@ ### 하이라이트 참조 — PDF 위치 링크 - 사용자가 Logseq PDF 뷰어에서 하이라이트를 만들면 `pages/hls__.md`에 블록이 생긴다 (`id:: `, `hl-page:: <쪽>` 속성 포함). -- Claude는 hls 페이지를 **읽기만** 하고, 정리 본문의 관련 개념 옆에 블록 참조 `((uuid))`를 삽입한다. 클릭하면 PDF의 정확한 위치로 이동한다. +- Claude는 hls 페이지를 **읽기만** 하고, 정리 본문의 관련 개념 아래에 자식 블록으로 참조를 삽입한다. 형식: `- 📌 원문 <설명> (p.쪽): ((uuid))`. 클릭하면 PDF의 정확한 위치로 이동한다. +- 하이라이트 위치 파악: `hl-page::`는 **PDF 내부 쪽번호**라서 책의 인쇄 쪽번호와 오프셋이 있을 수 있다 (1장 PDF는 책 쪽 = hl-page + 18). 같은 쪽에 하이라이트가 여러 개면 `assets/.edn`의 `:y1` 좌표로 상하 순서를 구분한다. - 배치 기준: 개념 정의, 핵심 정리(定理), 중요 예제 등 **원문 대조가 유용한 지점에만** 넣는다. 남발하지 않는다. -- Claude는 하이라이트를 **직접 생성하지 않는다** (`assets/*.edn`에 렌더링 좌표를 써야 해서 불안정하고, 앱 캐시 롤백과 충돌 위험). 정리 중 원문 링크가 필요한데 해당 하이라이트가 없으면, 정리 완료 보고 시 **하이라이트 요청 목록**(쪽 번호 + 해당 문구)을 정리해 사용자에게 알린다. 사용자가 하이라이트를 만든 뒤 다시 요청하면 그때 `((uuid))` 참조를 채워 넣는다. -- 그림·도표는 사용자가 **영역(area) 하이라이트**로 만들어두면 참조 시 이미지로 렌더링된다. 영역 하이라이트가 있으면 별도 추출 없이 그것을 우선 참조한다. +- Claude는 하이라이트를 **직접 생성하지 않는다** (`assets/*.edn`에 렌더링 좌표를 써야 해서 불안정하고, 앱 캐시 롤백과 충돌 위험). 원문 링크가 필요한데 하이라이트가 없는 지점은 작업 흐름 4단계의 **하이라이트 요청 목록**으로 제안한다. +- 그림·도표·수식 박스는 사용자가 **영역(area) 하이라이트**로 만들어두면 참조 시 이미지로 렌더링된다. 영역 하이라이트가 있으면 별도 추출 없이 그것을 우선 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P{`@AAcC&ei4oLq$=T2RI literal 0 HcmV?d00001 diff --git a/pages/1장 벡터와 행렬.md b/pages/1장 벡터와 행렬.md index a9e13b1..d2c8d8e 100755 --- a/pages/1장 벡터와 행렬.md +++ b/pages/1장 벡터와 행렬.md @@ -7,6 +7,7 @@ deck:: Logseq/전공공부/선형대수학 - ① 모든 선형결합 $Ax = x_1v_1 + x_2v_2 + \cdots + x_nv_n$ 은 어떤 모양(직선/평면/공간)을 채우는가? → **열공간** (1.3절) - ② 원하는 출력 $b$ 를 만드는 수 $x_1, \dots, x_n$ 을 찾을 수 있는가? → **선형방정식** $Ax=b$ (2장에서 본격적으로) - ## 1.1 벡터와 선형결합 + - 📌 원문 요약 박스 (p.21): ((6a5b74dd-cab9-4dcd-92c2-1cbaf5c9fc6c)) - ### 핵심 개념 - **선형결합** (linear combination): 임의의 수 $c, d$ 에 대한 $cv + dw$ 형태. - 벡터의 2가지 기본 연산을 합친 것: **수 곱하기** ($3v$) + **같은 차원끼리 더하기** ($v+w$). @@ -20,6 +21,7 @@ deck:: Logseq/전공공부/선형대수학 - **열 방법**: 선형결합 $c \begin{bmatrix} v_1 \\ v_2 \end{bmatrix} + d \begin{bmatrix} w_1 \\ w_2 \end{bmatrix} = b$ - **행 방법**: $c, d$ 에 대한 방정식 2개 - **행렬 방법**: $\begin{bmatrix} v_1 & w_1 \\ v_2 & w_2 \end{bmatrix} \begin{bmatrix} c \\ d \end{bmatrix} = b$ + - 📌 원문 표 (p.23): ((6a5b74f6-a99c-4df9-857c-944875fdbec4)) - **소거법**: 한 방정식에서 다른 방정식의 배수를 빼서 좌변에 0을 만든다 → 미지수 하나 소거 → 역대입. - 첫 방정식에 0이 있어 소거가 어려워 보이면 **방정식 순서를 바꾸면** 된다. - **소거법이 실패하는 경우** = 해가 없는 경우뿐이다. @@ -59,6 +61,8 @@ deck:: Logseq/전공공부/선형대수학 - ## 1.2 내적으로부터의 길이와 각 - ### 핵심 개념 - **내적** (dot product): $v \cdot w = v_1 w_1 + v_2 w_2 + \cdots + v_n w_n$. 순서는 무관: $v \cdot w = w \cdot v$. + - 📌 원문 정의 — 2차원 식 (1) (p.31): ((6a5b750f-8720-4ae8-b8d5-2399b6c6cb65)) + - 📌 원문 정의 — $n$ 차원 식 (2) (p.31): ((6a5b7514-9a2e-4601-ab79-a26e887561a0)) - **길이** (length): $\|v\| = \sqrt{v \cdot v} = \sqrt{v_1^2 + \cdots + v_n^2}$. - 피타고라스 정리의 $n$ 차원 확장. 차원을 하나씩 추가하며 직각삼각형을 반복 적용한다. - $n$ 차원 단위정육면체의 대각선 길이는 $\sqrt{n}$ (예: $(1,1,1,1)$ 의 길이는 2). @@ -75,10 +79,12 @@ deck:: Logseq/전공공부/선형대수학 - **코사인 공식** (cosine formula): $v, w$ 가 영벡터가 아닐 때 - $$\cos\theta = \frac{v \cdot w}{\|v\| \|w\|}$$ - 단위벡터끼리라면 그냥 $\cos\theta = u \cdot U$. 삼각법의 $\cos(\beta - \alpha) = \cos\alpha\cos\beta + \sin\alpha\sin\beta$ 가 배경. + - 📌 원문 식 (5) (p.35): ((6a5b752c-fe72-4e43-b869-f6d77622c379)) - $|\cos\theta| \le 1$ 로부터 얻는, 수학에서 가장 중요한 2가지 부등식: - **슈바르츠 부등식** (Schwarz inequality): $|v \cdot w| \le \|v\| \|w\|$ - **삼각부등식** (triangle inequality): $\|v+w\| \le \|v\| + \|w\|$ — 삼각형의 한 변은 나머지 두 변의 합을 초과할 수 없다. - 삼각부등식은 슈바르츠 부등식으로부터 유도: $\|v+w\|^2 \le \|v\|^2 + 2\|v\|\|w\| + \|w\|^2 = (\|v\|+\|w\|)^2$. + - 📌 원문 박스 (p.36): ((6a5b7538-a296-44b4-9477-21b6393c05ce)) - 응용 예: - 경제 (EX 5): 총비용 = (수량 벡터 $q$) $\cdot$ (가격 벡터 $p$). 내적이 0이면 장부의 균형 (수입 = 지출). - 기하평균 ≤ 산술평균 (EX 8): $v=(a,b)$, $w=(b,a)$ 에 슈바르츠를 적용하면 $2ab \le a^2 + b^2$, 즉 $|ab| \le \frac{1}{2}(a^2+b^2)$. @@ -128,18 +134,21 @@ deck:: Logseq/전공공부/선형대수학 - **열공간** (column space) $C(A)$: 모든 벡터 $Ax$, 즉 열들의 **모든 선형결합**의 집합. - **생성** (span): 벡터 집합의 모든 선형결합. "행렬 $A$ 의 열의 생성 = 열공간". - 방정식과의 연결: $Ax = b$ 는 $b$ 가 $C(A)$ 에 있을 때 해 $x$ 를 갖는다. + - 📌 원문 박스 (p.46): ((6a5b7553-d1c5-49ea-b1e1-e9b008137458)) - $m = 3$ (열들이 3차원 벡터)일 때 열공간으로 가능한 4가지: - ① 전체 공간 $\mathbb{R}^3$ — 선형독립인 열 3개 - ② 원점을 지나는 평면 — 선형독립인 열 2개 - ③ 원점을 지나는 직선 — 선형독립인 열 1개 - ④ 점 $(0,0,0)$ — $A$ 가 영행렬 - ⚠️ 열공간은 **항상 원점을 포함**한다 ($x = 0$ 이면 $Ax = 0$). + - 📌 원문 — 4가지 경우 (p.48): ((6a5b7574-72d1-4ac2-bb64-3f37b95a3f5e)) - **랭크** (rank) $r$: 선형독립인 열의 개수. 열공간의 "실제 크기". - **랭크 1 행렬**: 모든 열이 동일한 직선 위 → 열공간이 원점을 지나는 직선. - 놀라운 사실: 이때 **모든 행도 하나의 직선 위**에 있다 (모든 행이 한 행의 상수배). - $2 \times 2$ 로 확인: 2열이 1열의 $m$ 배인 $\begin{bmatrix} a & ma \\ b & mb \end{bmatrix}$ 에서 2행 $[b \ mb]$ 는 1행 $[a \ ma]$ 의 $\frac{b}{a}$ 배. - → **행 랭크 = 열 랭크** (선형대수학의 첫 번째 위대한 정리). 랭크 1은 여기서 확인, 일반 증명은 1.4절 $A = CR$ 로. - 1.4절로 가는 질문들 (p.48): 독립인 열은 몇 개인가(= 랭크 $r$)? 처음 $r$ 개의 독립인 열은(= 열공간의 **기저**)? $A$ 를 어떻게 $CR$ 로 분해하는가? + - 📌 원문 질문 박스 (p.48): ((6a5b7579-424b-4e07-9595-4adb2c4014fa)) - ### ❓ 스스로 점검 - $Ax$ 를 "열을 이용한 방법"으로 설명하라. - $Ax$ 는 $A$ 의 열들의 선형결합 $x_1 a_1 + \cdots + x_n a_n$ 이다. $x$ 의 성분들이 각 열의 계수가 된다. @@ -187,6 +196,7 @@ deck:: Logseq/전공공부/선형대수학 - $R$ 의 역할: $C$ 의 열들을 어떻게 결합하면 $A$ 의 각 열이 나오는지 기록. $(A$ 의 $j$ 열$) = C \times (R$ 의 $j$ 열$)$. - $R = [I \ F]$ 구조: $C$ 로 들어간 열 위치에 항등행렬 $I$, 종속인 열 위치에 결합 계수 ($F$). - 예 (p.60): $\begin{bmatrix} 2 & 6 & 4 \\ 4 & 12 & 8 \\ 1 & 3 & 5 \end{bmatrix} = \begin{bmatrix} 2 & 4 \\ 4 & 8 \\ 1 & 5 \end{bmatrix} \begin{bmatrix} 1 & 3 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ — 2열 = 3(1열) 이라 $C$ 에서 제외, $R$ 의 2열에 계수 3. + - 📌 원문 정리 ❶❷❸ (p.60): ((6a5b7591-28ea-4a27-896d-360fd2f1725b)) - 모든 열이 선형독립이면 $C = A$, $R = I$. - $R$ **을 찾는 방법 — 소거법** (행 축소, row reduction): - 행 연산(한 행에서 다른 행의 배수 빼기)으로 $A$ 를 단순화 → 상삼각행렬 $U$ → 위쪽 행까지 계속 소거 → $R_0$ (**기약행 사다리꼴**, reduced row echelon form, MATLAB의 rref(A)). @@ -200,6 +210,7 @@ deck:: Logseq/전공공부/선형대수학 - ④ $A$ 의 모든 행은 $R$ 의 행들의 선형결합 ($A = CR$) - $A = CR$ 에 관한 주요 사실: $C$ 의 $r$ 개 열은 $A$ 의 **열공간의 기저**, $R$ 의 $r$ 개 행은 $A$ 의 **행공간의 기저** ('기저'·'차원'의 정식 정의는 3.4절). - $C$ 는 $A$ 와 동일한 열공간을, $R$ 은 $A$ 와 동일한 행공간을 갖는다. + - 📌 원문 박스 (p.63): ((6a5b75a0-8bcd-4080-b864-6cefab1bb900)) - ⚠️ **주의**: $C$ 는 $A$ 의 열을 **그대로** 가져오지만, $R$ 은 $A$ 의 행을 그대로 가져온 것이 **아니다** ($R$ 의 행은 $A$ 의 행들의 선형결합). - ### ❓ 스스로 점검 - $AB$ 의 $j$ 열은 무엇인가? diff --git a/pages/hls__1장_벡터와_행렬_1784335993046_0.md b/pages/hls__1장_벡터와_행렬_1784335993046_0.md index 889c845..1470e29 100755 --- a/pages/hls__1장_벡터와_행렬_1784335993046_0.md +++ b/pages/hls__1장_벡터와_행렬_1784335993046_0.md @@ -1,2 +1,80 @@ file:: [1장_벡터와_행렬_1784335993046_0.pdf](../assets/1장_벡터와_행렬_1784335993046_0.pdf) file-path:: ../assets/1장_벡터와_행렬_1784335993046_0.pdf + +- [:span] + ls-type:: annotation + hl-page:: 3 + hl-color:: blue + id:: 6a5b74dd-cab9-4dcd-92c2-1cbaf5c9fc6c + hl-type:: area + hl-stamp:: 1784378586870 +- [:span] + ls-type:: annotation + hl-page:: 5 + hl-color:: blue + id:: 6a5b74f6-a99c-4df9-857c-944875fdbec4 + hl-type:: area + hl-stamp:: 1784378612799 +- [:span] + ls-type:: annotation + hl-page:: 13 + hl-color:: blue + id:: 6a5b750f-8720-4ae8-b8d5-2399b6c6cb65 + hl-type:: area + hl-stamp:: 1784378637852 +- [:span] + ls-type:: annotation + hl-page:: 13 + hl-color:: blue + id:: 6a5b7514-9a2e-4601-ab79-a26e887561a0 + hl-type:: area + hl-stamp:: 1784378643210 +- [:span] + ls-type:: annotation + hl-page:: 17 + hl-color:: blue + id:: 6a5b752c-fe72-4e43-b869-f6d77622c379 + hl-type:: area + hl-stamp:: 1784378667056 +- [:span] + ls-type:: annotation + hl-page:: 18 + hl-color:: blue + id:: 6a5b7538-a296-44b4-9477-21b6393c05ce + hl-type:: area + hl-stamp:: 1784378677540 +- [:span] + ls-type:: annotation + hl-page:: 28 + hl-color:: blue + id:: 6a5b7553-d1c5-49ea-b1e1-e9b008137458 + hl-type:: area + hl-stamp:: 1784378705862 +- [:span] + ls-type:: annotation + hl-page:: 30 + hl-color:: blue + id:: 6a5b7574-72d1-4ac2-bb64-3f37b95a3f5e + hl-type:: area + hl-stamp:: 1784378738809 +- [:span] + ls-type:: annotation + hl-page:: 30 + hl-color:: blue + id:: 6a5b7579-424b-4e07-9595-4adb2c4014fa + hl-type:: area + hl-stamp:: 1784378743733 +- [:span] + ls-type:: annotation + hl-page:: 42 + hl-color:: blue + id:: 6a5b7591-28ea-4a27-896d-360fd2f1725b + hl-type:: area + hl-stamp:: 1784378767689 +- [:span] + ls-type:: annotation + hl-page:: 45 + hl-color:: blue + id:: 6a5b75a0-8bcd-4080-b864-6cefab1bb900 + hl-type:: area + hl-stamp:: 1784378783139 \ No newline at end of file

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