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— Kunal
Miscellaneous math definitions
Notes from some courses I was taking / books I was reading; originally written to work well in logseq and now squashed together for legibility. I'll probably convert these to Anki soon. (From BRML, MML)
Abelian
- A group that is also commutative; eg. integers + addition operation
Adjacency Matrix
- A[ij] = 1 if there is an edge from node i to node j.
- Choose 1/0 in the diagonal.
- Symmetric for undirected graphs.
- Labeling nodes in ancestral order allows for a triangular adjacency matrix.
Chord
- Edge connecting 2 non adjacent nodes in a loop
Coordinate System
- Translate coordinates to vectors.
Connected Graph
- Undirected graph with a path between every pair of nodes.
Clique
- Fully connected subset of nodes in an undirected graph; all members are neighbours.
Clique Matrix
- Each column has 1s describing nodes which are part of a maximal clique.
Cliquo
Cliquo Matrix
- Clique Matrix that relaxes the condition that each clique is a maximal clicque.
Cycle
- Directed path that starts and returns to the same node.
Eigenbasis
- Eigen vectors that are also basis vectors
Linearly Dependent
- One of the vectors can be expressed as a linear combination of other vectors
Logit
- log(probability / 1 - probability)
Loop
- Path conneting more than 2 nodes, irrespective of edge direction; starts and returns to the same node.
Maximal Clique
- No larger Clique contains the nodes in the given clique.
Multiply Connected Graph
- Multiple paths between any node and another node.
Path
- Sequence of nodes that connects first note to second note.
Pivot
- First non zero variable in row echelon matrix, also leading coefficient
- A matrix is in row echelon
- all only zero rows are at the bottom
- for all non zero rows, the first nonzero number (pivot) is strictly to the right of the pivot above it
Singly Connected Graph
- Only one path from any node to another node.