From e6faf2c3d54d9990141ad40ea60cbd31e8b46a0a Mon Sep 17 00:00:00 2001 From: songyc macbook Date: Mon, 24 Aug 2026 18:33:46 +0900 Subject: [PATCH] =?UTF-8?q?=EB=B3=B5=EC=8A=B5=20=EC=A4=91=20=EC=88=98?= =?UTF-8?q?=EC=A0=95=EB=B6=84=20=EB=B0=98=EC=98=81:=203.1=C2=B73.2=20?= =?UTF-8?q?=EC=A0=90=EA=B2=80=20=EB=AC=B8=EA=B5=AC=20=EB=8B=A4=EB=93=AC?= =?UTF-8?q?=EA=B8=B0,=204.5=20=EC=9A=94=EC=95=BD=ED=91=9C=20=EC=9D=B4?= =?UTF-8?q?=EB=AF=B8=EC=A7=80=20=EC=B9=B4=EB=93=9C=ED=99=94(=EB=B9=88?= =?UTF-8?q?=EC=B9=B8/=EC=A0=95=EB=8B=B5=20SVG=C2=B7PNG=20=EC=B6=94?= =?UTF-8?q?=EA=B0=80),=20CLAUDE.md=20=EC=A7=84=ED=96=89=20=EC=83=81?= =?UTF-8?q?=ED=99=A9=20=EA=B0=B1=EC=8B=A0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-Authored-By: Claude Fable 5 Claude-Session: https://claude.ai/code/session_018JYaHeD41WPAk5P5wBojQe --- CLAUDE.md | 8 +++- .../1장_벡터와_행렬_1784335993046_0.edn | 2 +- ..._선형방정식_Ax_=_b_풀기_1784805780272_0.edn | 2 +- ...장_4가지_기본_부분공간_1785222523974_0.edn | 2 +- Major Study/assets/4장_4.5_요약표_빈칸.png | Bin 0 -> 57970 bytes Major Study/assets/4장_4.5_요약표_빈칸.svg | 24 ++++++++++ Major Study/assets/4장_4.5_요약표_정답.png | Bin 0 -> 116456 bytes Major Study/assets/4장_4.5_요약표_정답.svg | 45 ++++++++++++++++++ .../assets/solution_1784335983942_0.edn | 2 +- Major Study/pages/3.1 벡터공간과 부분공간.md | 8 ++-- .../3.2 소거법을 이용한 영공간 계산 A = CR.md | 8 ++-- Major Study/pages/4.5 행렬의 유사역행렬.md | 25 ++++------ 12 files changed, 98 insertions(+), 28 deletions(-) create mode 100755 Major Study/assets/4장_4.5_요약표_빈칸.png create mode 100755 Major Study/assets/4장_4.5_요약표_빈칸.svg create mode 100755 Major Study/assets/4장_4.5_요약표_정답.png create mode 100755 Major Study/assets/4장_4.5_요약표_정답.svg diff --git a/CLAUDE.md b/CLAUDE.md index 52aaed7..ebafb5f 100755 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -149,7 +149,13 @@ disable-anki-sync:: true - **해답집**: `Major Study/assets/solution_1784335983942_0.pdf` — 스트랭 6판 공식 영문 솔루션 (전 챕터). 문제 번호는 한국어판과 동일하다. 각 챕터의 "Problem Set x.y" 헤더로 위치를 찾는다 (1장 해답: PDF 2~18쪽). - **PDF 읽는 법**: 단원 PDF는 스캔+OCR본이라 텍스트 레이어의 수식이 깨져 있다. 정리할 때는 **Read 도구로 페이지를 시각적으로 읽는다** (pdftoppm/poppler 설치됨). 이미지 추출·edn 좌표 파싱은 PyMuPDF(`import fitz`, 설치됨)를 쓴다. - **쪽번호 오프셋**: 1장 PDF는 책 쪽번호 = PDF 쪽번호 + 18. 2장 PDF는 책 쪽번호 = PDF 쪽번호 + 70. 단원 PDF마다 오프셋이 다를 수 있으니 첫 몇 쪽으로 확인할 것. -- **진행 상황**: **1~3장 완전히 완료** (3장: 정리·복습·카드 19장 추가, 총 65장. 2026-08-06 싱크 검증 통과). 그래프 3분할·Anki 프로파일 3분할·모델명 이전·AnkiWeb 계정 분리·모바일 Working Copy 전환 모두 완결. 다음 신규 단원: **4장** — 소단원별 사이클 + GoodNotes 참고 플로우 첫 적용 (사용자가 깨끗한 스캔 PDF를 세팅해 오면 ① 링크 전 검증 필수, ② 쪽번호 오프셋 새로 확인, ③ 절마다 `bak/goodnotes/`의 GoodNotes 내보내기를 읽어 필기·여백 메모를 정리에 반영, ④ 선행 개념은 수위 조절 규칙 적용). 3장 쪽번호 오프셋은 책 쪽 = PDF 쪽 + 130 이었음. 2장에서 확립되어 이후 장에도 적용할 방식: ① 새 행렬의 **정확한 형태를 🧩 표시 블록으로 명시**, ② 「단순 요약 금지」의 쉬운 재구성 원칙(숫자 예제 먼저·단계 지도·흔한 오해 교정), ③ 필요시 자작 SVG 그림. 복습 중 사용자가 이해 안 되는 부분을 요청하면 해당 블록만 보강하는 패턴이 반복된다. +- **진행 상황 (2026-08-20 기준)**: **1~4장 정리 완료.** 1~3장은 카드화·싱크 검증까지 완결 (3장 카드 총 65장, 2026-08-06 싱크 검증 통과). 4장은 소단원별 사이클 + GoodNotes 플로우 첫 적용으로 4.1~4.5 정리·고찰·「이 단원 핵심문제」·카드화까지 완료 (4.5 카드 14장: #card 10 + cloze 블록 4). 그래프 3분할·Anki 프로파일 3분할·모델명 이전·AnkiWeb 계정 분리·모바일 Working Copy 전환 모두 완결. **현재 단계: 사용자가 1~4장 「이 단원 핵심문제」를 순회하며 복습 중** — 해설 추가·보강 요청과 개념 질문이 오면 대응한다 (질문에 "수정하지 말고 답변만"이 붙으면 파일을 건드리지 않는다). 남은 뒷정리: ① 4장 복습까지 끝나 완전 종료가 확인되면 `bak/goodnotes/`의 4장 GoodNotes PDF 전부 삭제, ② 사용자 Anki 싱크 시 Major Study 프로파일·create 수 검증. 다음 신규 단원: **5장** (소단원별 사이클 계속). 3장 쪽번호 오프셋은 책 쪽 = PDF 쪽 + 130 이었음. 2장에서 확립되어 이후 장에도 적용할 방식: ① 새 행렬의 **정확한 형태를 🧩 표시 블록으로 명시**, ② 「단순 요약 금지」의 쉬운 재구성 원칙(숫자 예제 먼저·단계 지도·흔한 오해 교정), ③ 필요시 자작 SVG 그림. 복습 중 사용자가 이해 안 되는 부분을 요청하면 해당 블록만 보강하는 패턴이 반복된다. +- ## 단원 PDF 내보내기 (아이디어, 요청 시 구현) +- 사용자가 "n단원 pdf로 만들어줘"라고 하면, 그 단원 페이지 + 거기 링크된 소단원 페이지들을 묶어 Logseq에서 보이는 느낌의 PDF 한 부로 만든다 (2026-08-20 가능성만 확인해 둔 상태, **아직 미구현**. 사용자가 필요할 때 요청하기로 함). +- 파이프라인: ① 단원 페이지에서 `[[x.y ...]]` 링크를 수집해 페이지 목록 구성 → ② Logseq 문법 전처리: 속성 줄(`id::`·`deck::`·`collapsed::` 등) 숨김, `{{c1 ...}}` cloze는 괄호 벗겨 일반 텍스트화, `((uuid))`는 hls 페이지에서 원문 텍스트를 찾아 "📌 ... (p.n)"으로 치환, `../assets/` 이미지 경로 절대경로화 → ③ 불릿 계층 CSS(흰 배경, Logseq풍) + KaTeX 수식 렌더링 HTML 생성 → ④ Chrome 헤드리스 `--headless --print-to-pdf`로 변환. +- 이 맥 환경: pandoc·xelatex·wkhtmltopdf·weasyprint 없음, **Google Chrome 있음** (추가 설치 없이 가능. 2026-08-20 확인). +- 한계 (사용자에게 안내 완료): 스캔 원본 PDF 임베드는 못 넣으니 링크 한 줄로 대체, 블록 접기·하이라이트 점프 등 인터랙션 없음 (전부 펼친 상태로 인쇄). +- 산출물 PDF는 그래프 `assets/`에 넣지 말고 스크래치나 `bak/` 등 git 밖에 만들어 전달한다. 첫 요청 때는 한 장짜리 시범본으로 스타일을 확인받고 조정한다. - ## Logseq 앱 동기화 주의 - Logseq 앱이 페이지를 열어둔 상태에서 파일을 밖에서 수정하면, 앱이 캐시된 옛 블록을 표시하다가 **옛 내용을 파일에 되써버릴 수 있다** (부분 롤백 발생). - 페이지 파일을 수정한 후에는 사용자에게 **Logseq 재색인(Re-index)** 을 안내한다. 수정 직후 "고쳤는데 그대로다"라는 피드백이 오면 파일을 다시 읽어 롤백 여부부터 확인한다. diff --git a/Major Study/assets/1장_벡터와_행렬_1784335993046_0.edn b/Major Study/assets/1장_벡터와_행렬_1784335993046_0.edn index 1c34062..3f9046d 100755 --- a/Major Study/assets/1장_벡터와_행렬_1784335993046_0.edn +++ b/Major Study/assets/1장_벡터와_행렬_1784335993046_0.edn @@ -130,4 +130,4 @@ :page 45}, :content {:text "[:span]", :image 1784378783139}, :properties {:color "blue"}}], - :extra {:page 5}} + :extra {:page 49}} diff --git a/Major Study/assets/2장_선형방정식_Ax_=_b_풀기_1784805780272_0.edn b/Major Study/assets/2장_선형방정식_Ax_=_b_풀기_1784805780272_0.edn index 7543028..7e2d093 100755 --- a/Major Study/assets/2장_선형방정식_Ax_=_b_풀기_1784805780272_0.edn +++ b/Major Study/assets/2장_선형방정식_Ax_=_b_풀기_1784805780272_0.edn @@ -1171,4 +1171,4 @@ :page 55}, :content {:text "[:span]", :image 1784898936929}, :properties {:color "yellow"}}], - :extra {:page 60}} + :extra {:page 25}} diff --git a/Major Study/assets/3장_4가지_기본_부분공간_1785222523974_0.edn b/Major Study/assets/3장_4가지_기본_부분공간_1785222523974_0.edn index f3454ef..ba109f7 100755 --- a/Major Study/assets/3장_4가지_기본_부분공간_1785222523974_0.edn +++ b/Major Study/assets/3장_4가지_기본_부분공간_1785222523974_0.edn @@ -1899,4 +1899,4 @@ :page 65}, :content {:text "[:span]", :image 1785863457636}, :properties {:color "yellow"}}], - :extra {:page 2}} + :extra {:page 25}} diff --git a/Major Study/assets/4장_4.5_요약표_빈칸.png 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z$@=U9H8d)_ySo+bl@yN)^4(!^*8u-w8nm*76Iu4f3$t6+u#>z3Qu9*<{x!Cuu3qj5 zurb$HNlB-#)Xs;BIsyCoD!Ye=73~$3@SA$57ilE9?{NbThvV^ZHKGErGLLSN4m){%Xqx2KPlFN=tCtylRJD*?J5s{2gP~}MUH$LUv%pAQ8JR}I|1J^7o(Xg=dItP0 zne@LmG*H + + + + + + + + + + + + +유형 +판정 +A+ 공식 +A+A +AA+ +A+b 의 의미 +정사각 가역 +r = m = n +A-1 +I +I +유일한 해 +세로 (열 독립) +r = n < m +(ATA)-1AT +I +Pcol +최소제곱해 x̂ +가로 (행 독립) +r = m < n +AT(AAT)-1 +Prow +I +최단 해 x+ +일반 (둘 다 부족) +r < m, r < n +R+C+ = RT(CTART)-1CT +Prow +Pcol +최소노름 +최소제곱해 + \ No newline at end of file diff --git a/Major Study/assets/solution_1784335983942_0.edn b/Major Study/assets/solution_1784335983942_0.edn index ab9a38b..c59f749 100755 --- a/Major Study/assets/solution_1784335983942_0.edn +++ b/Major Study/assets/solution_1784335983942_0.edn @@ -1 +1 @@ -{:highlights [], :extra {:page 1}} +{:highlights [], :extra {:page 21}} diff --git a/Major Study/pages/3.1 벡터공간과 부분공간.md b/Major Study/pages/3.1 벡터공간과 부분공간.md index a03e41c..d301c9c 100755 --- a/Major Study/pages/3.1 벡터공간과 부분공간.md +++ b/Major Study/pages/3.1 벡터공간과 부분공간.md @@ -50,7 +50,7 @@ deck:: Logseq/전공공부/선형대수학 - 📌 원문 (p.137): ((6a6860d3-efc3-4506-a1d2-ad1b12720150)) - $Ax = b$ **의 해가 존재한다** ⟺ $b \in \mathbf{C}(A)$. 이때 그 선형결합의 계수가 바로 해 $x$ 다. - 📌 원문 (p.137): ((6a6860eb-b4f8-478f-99f2-5be30d4bd98a)) - - ⚠️ **흔한 혼동, "열들의 집합"과 "열공간"은 다르다** (사용자 요청으로 자세히): + - ⚠️ **흔한 혼동, "열들의 집합"과 "열공간"은 다르다** : - 📌 원문 (p.137): ((6a686110-e6d3-4d7d-a15d-1781c70e4791)) - **행렬** $A$ **의 열만 모으면 부분공간이 아니다**: $3 \times 3$ 행렬이면 열이 딱 3개, 벡터 3개짜리 유한집합이다. 부분공간이 되려면 $2 \times ($1열$)$, $($1열$) + ($2열$)$ 같은 **결합 결과가 전부** 들어 있어야 하는데 하나도 없다. 그래서 열들을 재료로 **모든 선형결합을 채워 넣어야** 비로소 열공간이 된다. 이 채워 넣는 행위가 **"생성"** 이다. - **가역행렬 전체의 집합은 (** $\mathbb{R}^{n\times n}$ **의) 부분공간이 아니다**: 두 가지 이유. ① 영행렬(이 공간의 영벡터)이 없다. 영행렬은 비가역이니까. ② 덧셈에 안 닫힌다: $I$ 와 $-I$ 는 둘 다 가역이지만 $I + (-I) = 0$ 은 비가역 → 합이 집합을 탈출. @@ -74,17 +74,17 @@ deck:: Logseq/전공공부/선형대수학 - 부분집합과 부분공간의 차이를 한 문장으로 말하라. #card id:: 6a746749-1723-4720-abdd-e57c5e916591 - 부분집합은 벡터들을 그냥 골라 담은 것(조건 없음), 부분공간은 그중 $v+w$ 와 $cv$ 에 닫혀 있어서 그 자체로 벡터공간이 되는 것. - - 부분공간 판정법 2가지는? 이것만 확인하면 8가지 조건은 왜 자동인가? #card + - 부분공간 판정법 2가지는? 이것만 확인하면 8가지 조건은 왜 자동으로 성립하는가? #card id:: 6a746749-05c4-49f2-95a8-e003d810edae - ① $v + w$ 가 안에 있다 ② $cv$ 가 안에 있다. - 연산 자체를 원래 벡터공간에서 물려받으므로 교환·결합법칙 등은 자동 성립. - - 왜 모든 부분공간은 영벡터를 포함해야 하는가? 이 사실로 즉시 탈락시킬 수 있는 집합의 예는? #card + - 왜 모든 부분공간은 영벡터를 포함해야 하는가? 이 사실로 즉시 부분공간에서 탈락시킬 수 있는 집합의 예는? #card id:: 6a746749-bc47-479e-a224-2248454ecf62 - 판정법 ②에 $c = 0$ 을 넣으면 $0v = 0$ 이 포함되어야 하기 때문. 원점을 지나지 않는 직선·평면은 즉시 탈락. - $\mathbb{R}^3$ 의 부분공간을 전부 나열하라. #card id:: 6a746749-5939-40fd-8bfb-acd80cc197f8 - $\mathbf{Z}$ (영벡터만), 원점 지나는 직선 $\mathbf{L}$, 원점 지나는 평면 $\mathbf{P}$, $\mathbb{R}^3$ 전체. - - 제1사분면은 어느 판정 조건에서 탈락하는가? 제1∪제3사분면은? #card + - 제1사분면은 어느 판정 조건에서 부분공간 조건에서 탈락하는가? 제1∪제3사분면은? #card id:: 6a746749-148c-4376-8b09-ac2a905582c6 - 제1사분면: 스칼라곱($c = -1$)에서 탈락. 제1∪제3사분면: 덧셈에서 탈락 (예: $(2,3)+(-3,-2) = (-1,1)$). - 열공간 $\mathbf{C}(A)$ 의 정의는? $Ax = b$ 의 해가 존재할 필요충분조건을 열공간의 언어로 말하라. diff --git a/Major Study/pages/3.2 소거법을 이용한 영공간 계산 A = CR.md b/Major Study/pages/3.2 소거법을 이용한 영공간 계산 A = CR.md index 0229331..d7e5d72 100755 --- a/Major Study/pages/3.2 소거법을 이용한 영공간 계산 A = CR.md +++ b/Major Study/pages/3.2 소거법을 이용한 영공간 계산 A = CR.md @@ -80,10 +80,10 @@ deck:: Logseq/전공공부/선형대수학 id:: 6a746749-88b2-4f5d-9783-0eabe50c24ad - 자유변수 하나에 1, 나머지 자유변수에 0을 넣고 피벗변수를 역대입으로 구한다. - $(n-r)$ 개가 나오고, 영공간 = 특별해들의 모든 선형결합 (특별해가 영공간의 기저). - - $[\,I\ \ F\,]x = 0$ 의 특별해를 행렬 하나로 표현하면? 검산은 왜 자동인가? + - $[\,I\ \ F\,]x = 0$ 의 특별해를 행렬 하나로 표현하면? 검산은 왜 자동으로 성립되는가? - $\begin{bmatrix} -F \\ I \end{bmatrix}$ 의 열들 (열 섞였으면 $P^{\mathrm{T}}$ 를 앞에). $[\,I\ F\,]\begin{bmatrix} -F \\ I \end{bmatrix} = -F + F = 0$ 이므로. - - $H = WF$ 에서 $W, H, F$ 는 각각 무엇인가? 책 p.147 박스의 오타는 무엇인가? - - $W$ = 독립인 열들, $H$ = 종속인 열들, $F$ = 독립을 결합해 종속을 만드는 계수(조리법). 박스는 "(독립 열) = (종속 열)×F"로 뒤바뀌어 인쇄됨. 올바른 방향은 (종속 열) = (독립 열)×F. + - $H = WF$ 에서 $W, H, F$ 는 각각 무엇인가? + - $W$ = 독립인 열들, $H$ = 종속인 열들, $F$ = 독립을 결합해 종속을 만드는 계수(조리법). - "$R_0$ 안의 $I$ 가 $C$ 의 위치를 알려준다"에서 '위치'란? $C$ 의 열은 어디서 가져오는가? - $I$ 를 이루는 피벗 열들의 열 번호. $C$ 의 열은 $R_0$ 가 아니라 $A$ **의 원본 열**을 그 번호대로 뽑아온다. - 왜 $\mathbf{N}(A) = \mathbf{N}(R_0)$ 인가? #card @@ -92,7 +92,7 @@ deck:: Logseq/전공공부/선형대수학 - 역으로 $EAx=0$ 이면 $E^{-1}$ 를 곱해 $Ax=0$. 해집합이 같다. - $n > m$ 이면 $Ax = 0$ 에 0 아닌 해가 반드시 존재하는 이유를 한 줄로. #card id:: 6a746749-1d39-461e-b847-283bb6520df7 - - 피벗 ≤ $m$ < $n$ → 자유변수 ≥ 1 → 특별해 존재. + - 피벗 ≤ $m$ < $n$ 이므로 자유변수가 최소 1개는 존재함. 이는 곧 특별해가 무조건 1개는 존재함을 의미. - ### ✏️ 연습문제 풀이 (솔루션 참고) - **문제 1** (카드화하기 좋은 문제): $E$ 가 가역행렬일 때, $A$ 와 $R = EA$ 는 왜 동일한 영공간을 갖는가? - 📌 문제 지문 (p.153): [🔗 PDF 위치](((6a6e8c28-2ec2-4994-a90e-16eeb55f3995))) diff --git a/Major Study/pages/4.5 행렬의 유사역행렬.md b/Major Study/pages/4.5 행렬의 유사역행렬.md index ee94ce2..9cc11a7 100755 --- a/Major Study/pages/4.5 행렬의 유사역행렬.md +++ b/Major Study/pages/4.5 행렬의 유사역행렬.md @@ -198,23 +198,18 @@ deck:: Logseq/전공공부/선형대수학 - $A$ 가 가역이면 $A^{+} = A^{-1}$ 로 일치한다. - $A^{+}$ 의 정의(행동강령 3줄)를 재현하라. $\mathbb{R}^m$ 의 벡터를 $y = b + z$ ($b \in$ 열공간, $z \in$ 좌영공간)로 직교 분해했을 때, $A^{+}$ 는 각 성분을 어디로 보내는가? - ① 열공간 성분 $b$ 는 {{c1 **행공간의 유일한 조상**}}으로 되돌린다 - extra:: $b = Ax$ 인 행공간의 $x$ 로, $A^{+}b = x$. id:: 6a869fdb-454b-4c05-bef8-d6acb5f42d9f - - ② 좌영공간 성분 $z$ 는 되돌릴 곳이 없으니 {{c1 **0**}} 으로 보낸다: - extra:: $A^{+}z = 0$. - id:: 6a86a0cc-2a76-4345-aaa5-e8a6a7311779 - - ③ 합치면 $A^{+}y$ = {{c1 $$A^{+}b + A^{+}z = x$$}} . 이 규칙 덕분에 $A^{+}b$ 는 언제나 {{c1 최소노름 최소제곱해}}가 된다. - id:: 6a86a0c6-3763-4c90-907e-1c3615d306bb - - 열 독립인 행렬은 어떤 모양인가? 반대로 행 독립인 경우에는? (가로로 긴지 세로로 긴지 답할 것.) + ② 좌영공간 성분 $z$ 는 되돌릴 곳이 없으니 {{c1 **0**}} 으로 보낸다: + ③ 합치면 $A^{+}y$ = {{c1 $$A^{+}b + A^{+}z = x$$}} . 이 규칙 덕분에 $A^{+}b$ 는 언제나 {{c1 최소노름 최소제곱해}}가 된다. + + #+BEGIN_EXTRA + $b = Ax$ 인 행공간의 $x$ 로, $A^{+}b = x$. + $A^{+}z = 0$. + #+END_EXTRA + - 다음의 표를 채우면? id:: 6a86998a-cbb6-4848-af8e-950a66edbb8d - 각 경우에 대한 판정과 $A^{+}$ 의 공식을 답하라. - 또한 어떤 경우에 각 공간의 사영행렬이 되는지도 답하라. 그리고 $A^{+}b$ 의 의미를 각각 답하라. #card - - | 유형 | 판정 | $A^{+}$ 공식 | $A^{+}A$ | $AA^{+}$ | $A^{+}b$ 의 의미 | - | --- | --- | --- | --- | --- | --- | - | 정사각 가역 | $r = m = n$ | $A^{-1}$ | $I$ | $I$ | 유일한 해 | - | 세로 (열 독립) | $r = n < m$ | $(A^{\mathrm{T}}A)^{-1}A^{\mathrm{T}}$ | $I$ | $P_{\text{col}}$ | 최소제곱해 $\hat{x}$ | - | 가로 (행 독립) | $r = m < n$ | $A^{\mathrm{T}}(AA^{\mathrm{T}})^{-1}$ | $P_{\text{row}}$ | $I$ | 최단 해 $x^{+}$ | - | 일반 (둘 다 부족) | $r < m,\ r < n$ | $R^{+}C^{+} = R^{\mathrm{T}}(C^{\mathrm{T}}AR^{\mathrm{T}})^{-1}C^{\mathrm{T}}$ | $P_{\text{row}}$ | $P_{\text{col}}$ | 최소노름 최소제곱해 | + ![A⁺ 유형별 요약표 (빈칸)](../assets/4장_4.5_요약표_빈칸.png) #card + - ![A⁺ 유형별 요약표 (정답)](../assets/4장_4.5_요약표_정답.png) - $A^{+}b$ 는 무엇을 주는가? 세 상황(해가 없다, 해가 무한하다, 둘 다)으로 나눠 말하라. #card id:: 6a85e662-9e46-45fb-9eb6-80b0aa180c03 - 해가 없을 수 있는 상황 (세로, $r = n$): 오차 $\|Ax - b\|$ 를 최소로 하는 **최소제곱해** $\hat{x}$ (정규방정식의 해).