---
type: CKG Bundle
title: Linear Algebra
tags: [STEM & Engineering]
timestamp: 2026-06-18T00:00:00Z
ckg:
  id: linear-algebra
  nodes: 300
  license: CC BY 4.0
---

# Linear Algebra — Compressed Knowledge Graph

```csv
ConceptID,ConceptLabel,TaxonomyID
1,Scalar,FOUND
2,Vector,FOUND
3,Vector Notation,FOUND
4,2D Vector,FOUND
5,3D Vector,FOUND
6,N-Dimensional Vector,FOUND
7,Vector Addition,FOUND
8,Scalar Multiplication,FOUND
9,Vector Subtraction,FOUND
10,Dot Product,FOUND
11,Cross Product,FOUND
12,Vector Magnitude,FOUND
13,Unit Vector,FOUND
14,Vector Normalization,FOUND
15,Euclidean Distance,FOUND
16,L1 Norm,FOUND
17,L2 Norm,FOUND
18,L-Infinity Norm,FOUND
19,Linear Combination,FOUND
20,Span,FOUND
21,Linear Independence,FOUND
22,Linear Dependence,FOUND
23,Basis Vector,FOUND
24,Standard Basis,FOUND
25,Coordinate System,FOUND
26,Vector Space,FOUND
27,Dimension of Space,FOUND
28,Matrix,MATOP
29,Matrix Notation,MATOP
30,Matrix Dimensions,MATOP
31,Row Vector,MATOP
32,Column Vector,MATOP
33,Matrix Entry,MATOP
34,Matrix Addition,MATOP
35,Matrix Scalar Multiply,MATOP
36,Matrix-Vector Product,MATOP
37,Matrix Multiplication,MATOP
38,Matrix Transpose,MATOP
39,Symmetric Matrix,MATOP
40,Identity Matrix,MATOP
41,Diagonal Matrix,MATOP
42,Triangular Matrix,MATOP
43,Upper Triangular,MATOP
44,Lower Triangular,MATOP
45,Orthogonal Matrix,MATOP
46,Matrix Inverse,MATOP
47,Invertible Matrix,MATOP
48,Sparse Matrix,MATOP
49,Dense Matrix,MATOP
50,Block Matrix,MATOP
51,Linear Equation,LINSYS
52,System of Equations,LINSYS
53,Matrix Equation Form,LINSYS
54,Augmented Matrix,LINSYS
55,Gaussian Elimination,LINSYS
56,Row Operations,LINSYS
57,Row Swap,LINSYS
58,Row Scaling,LINSYS
59,Row Addition,LINSYS
60,Row Echelon Form,LINSYS
61,Reduced Row Echelon Form,LINSYS
62,Pivot Position,LINSYS
63,Pivot Column,LINSYS
64,Free Variable,LINSYS
65,Basic Variable,LINSYS
66,Solution Set,LINSYS
67,Unique Solution,LINSYS
68,Infinite Solutions,LINSYS
69,No Solution,LINSYS
70,Homogeneous System,LINSYS
71,Trivial Solution,LINSYS
72,Numerical Stability,LINSYS
73,Back Substitution,LINSYS
74,Function,TRANS
75,Linear Transformation,TRANS
76,Transformation Matrix,TRANS
77,Domain,TRANS
78,Codomain,TRANS
79,Image,TRANS
80,Rotation Matrix,TRANS
81,2D Rotation,TRANS
82,3D Rotation,TRANS
83,Scaling Matrix,TRANS
84,Uniform Scaling,TRANS
85,Non-Uniform Scaling,TRANS
86,Shear Matrix,TRANS
87,Reflection Matrix,TRANS
88,Projection,TRANS
89,Orthogonal Projection,TRANS
90,Composition of Transforms,TRANS
91,Kernel,TRANS
92,Null Space,TRANS
93,Range,TRANS
94,Column Space,TRANS
95,Rank,TRANS
96,Nullity,TRANS
97,Rank-Nullity Theorem,TRANS
98,Invertible Transform,TRANS
99,Change of Basis,TRANS
100,Basis Transition Matrix,TRANS
101,Determinant,DETERM
102,2x2 Determinant,DETERM
103,3x3 Determinant,DETERM
104,Cofactor Expansion,DETERM
105,Minor,DETERM
106,Cofactor,DETERM
107,Determinant Properties,DETERM
108,Multiplicative Property,DETERM
109,Transpose Determinant,DETERM
110,Singular Matrix,DETERM
111,Volume Scaling Factor,DETERM
112,Signed Area,DETERM
113,Cramers Rule,DETERM
114,Eigenvalue,EIGEN
115,Eigenvector,EIGEN
116,Eigen Equation,EIGEN
117,Characteristic Polynomial,EIGEN
118,Characteristic Equation,EIGEN
119,Eigenspace,EIGEN
120,Algebraic Multiplicity,EIGEN
121,Geometric Multiplicity,EIGEN
122,Diagonalization,EIGEN
123,Diagonal Form,EIGEN
124,Similar Matrices,EIGEN
125,Complex Eigenvalue,EIGEN
126,Spectral Theorem,EIGEN
127,Symmetric Eigenvalues,EIGEN
128,Power Iteration,EIGEN
129,Dominant Eigenvalue,EIGEN
130,Eigendecomposition,EIGEN
131,Matrix Factorization,DECOMP
132,LU Decomposition,DECOMP
133,Partial Pivoting,DECOMP
134,QR Decomposition,DECOMP
135,Gram-Schmidt QR,DECOMP
136,Householder QR,DECOMP
137,Cholesky Decomposition,DECOMP
138,Positive Definite Matrix,DECOMP
139,SVD,DECOMP
140,Singular Value,DECOMP
141,Left Singular Vector,DECOMP
142,Right Singular Vector,DECOMP
143,Full SVD,DECOMP
144,Compact SVD,DECOMP
145,Truncated SVD,DECOMP
146,Low-Rank Approximation,DECOMP
147,Matrix Rank,DECOMP
148,Numerical Rank,DECOMP
149,Condition Number,DECOMP
150,Abstract Vector Space,INPROD
151,Subspace,INPROD
152,Vector Space Axioms,INPROD
153,Inner Product,INPROD
154,Inner Product Space,INPROD
155,Norm from Inner Product,INPROD
156,Cauchy-Schwarz Inequality,INPROD
157,Orthogonality,INPROD
158,Orthogonal Vectors,INPROD
159,Orthonormal Set,INPROD
160,Orthonormal Basis,INPROD
161,Gram-Schmidt Process,INPROD
162,Projection onto Subspace,INPROD
163,Least Squares Problem,INPROD
164,Normal Equations,INPROD
165,Row Space,INPROD
166,Left Null Space,INPROD
167,Four Subspaces,INPROD
168,Pseudoinverse,INPROD
169,Feature Vector,MLBASE
170,Feature Matrix,MLBASE
171,Data Matrix,MLBASE
172,Covariance Matrix,MLBASE
173,Correlation Matrix,MLBASE
174,Standardization,MLBASE
175,PCA,MLBASE
176,Principal Component,MLBASE
177,Variance Explained,MLBASE
178,Scree Plot,MLBASE
179,Dimensionality Reduction,MLBASE
180,Linear Regression,MLBASE
181,Design Matrix,MLBASE
182,Ridge Regression,MLBASE
183,Lasso Regression,MLBASE
184,Regularization,MLBASE
185,Gradient Vector,MLBASE
186,Gradient Descent,MLBASE
187,Batch Gradient Descent,MLBASE
188,Learning Rate,MLBASE
189,Perceptron,NEURAL
190,Neuron Model,NEURAL
191,Activation Function,NEURAL
192,ReLU,NEURAL
193,Sigmoid,NEURAL
194,Tanh,NEURAL
195,Softmax,NEURAL
196,Weight Matrix,NEURAL
197,Bias Vector,NEURAL
198,Forward Propagation,NEURAL
199,Backpropagation,NEURAL
200,Chain Rule Matrices,NEURAL
201,Loss Function,NEURAL
202,Cross-Entropy Loss,NEURAL
203,Neural Network Layer,NEURAL
204,Hidden Layer,NEURAL
205,Deep Network,NEURAL
206,Convolutional Layer,NEURAL
207,Convolution Kernel,NEURAL
208,Stride,NEURAL
209,Padding,NEURAL
210,Pooling Layer,NEURAL
211,Batch Normalization,NEURAL
212,Layer Normalization,NEURAL
213,Tensor,NEURAL
214,Tensor Operations,NEURAL
215,Embedding,GENAI
216,Embedding Space,GENAI
217,Word Embedding,GENAI
218,Semantic Similarity,GENAI
219,Cosine Similarity,GENAI
220,Attention Mechanism,GENAI
221,Self-Attention,GENAI
222,Cross-Attention,GENAI
223,Query Matrix,GENAI
224,Key Matrix,GENAI
225,Value Matrix,GENAI
226,Attention Score,GENAI
227,Attention Weights,GENAI
228,Multi-Head Attention,GENAI
229,Transformer Architecture,GENAI
230,Position Encoding,GENAI
231,LoRA,GENAI
232,Latent Space,GENAI
233,Interpolation,GENAI
234,Hessian Matrix,OPTIM
235,Convexity,OPTIM
236,Convex Function,OPTIM
237,Newtons Method,OPTIM
238,Quasi-Newton Method,OPTIM
239,BFGS Algorithm,OPTIM
240,SGD,OPTIM
241,Mini-Batch SGD,OPTIM
242,Momentum,OPTIM
243,Adam Optimizer,OPTIM
244,RMSprop,OPTIM
245,Lagrange Multiplier,OPTIM
246,Constrained Optimization,OPTIM
247,KKT Conditions,OPTIM
248,Image Matrix,IMGPROC
249,Grayscale Image,IMGPROC
250,RGB Image,IMGPROC
251,Image Tensor,IMGPROC
252,Image Convolution,IMGPROC
253,Image Filter,IMGPROC
254,Blur Filter,IMGPROC
255,Sharpen Filter,IMGPROC
256,Edge Detection,IMGPROC
257,Sobel Operator,IMGPROC
258,Fourier Transform,IMGPROC
259,Frequency Domain,IMGPROC
260,Image Compression,IMGPROC
261,Color Space Transform,IMGPROC
262,Feature Detection,IMGPROC
263,Homography,IMGPROC
264,3D Coordinate System,GEOM3D
265,Euler Angles,GEOM3D
266,Gimbal Lock,GEOM3D
267,Quaternion,GEOM3D
268,Quaternion Rotation,GEOM3D
269,Homogeneous Coordinates,GEOM3D
270,Rigid Body Transform,GEOM3D
271,SE3 Transform,GEOM3D
272,Camera Matrix,GEOM3D
273,Intrinsic Parameters,GEOM3D
274,Extrinsic Parameters,GEOM3D
275,Projection Matrix,GEOM3D
276,Perspective Projection,GEOM3D
277,Stereo Vision,GEOM3D
278,Triangulation,GEOM3D
279,Epipolar Geometry,GEOM3D
280,Point Cloud,GEOM3D
281,LIDAR Point Cloud,AUTON
282,Camera Calibration,AUTON
283,Sensor Fusion,AUTON
284,Kalman Filter,AUTON
285,State Vector,AUTON
286,Measurement Vector,AUTON
287,Prediction Step,AUTON
288,Update Step,AUTON
289,Kalman Gain,AUTON
290,Extended Kalman Filter,AUTON
291,State Estimation,AUTON
292,SLAM,AUTON
293,Localization,AUTON
294,Mapping,AUTON
295,Object Detection,AUTON
296,Object Tracking,AUTON
297,Bounding Box,AUTON
298,Path Planning,AUTON
299,Motion Planning,AUTON
300,Trajectory Optimization,AUTON
```

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