Tree Data Structures and Matrix Inversion

This set covers key vocabulary for tree data structures and the mathematical process of matrix inversion based on the lecture notes.

Root Node

The top-most unique node in a tree structure, identified as node $1$ or node $A$ in the examples.

Edge

The connection between nodes, calculated by the formula $n - 1$, where $n$ is the total number of nodes.

Internal node

A node that has at least one child node.

Leaf node

A node with no children, where the height is always $0$. Examples include nodes $9, 14, 15, 6, 11, 13, 16$.

Siblings

Nodes that share the same parent node.

Degree of tree

The maximum number of children associated with any single node in the tree.

Height/Depth of tree

The maximum level reached by the tree, such as level $4$ in a tree with $16$ nodes.

Ancestor

The preceding nodes in a path from the root to a specific node (e.g., for node $E$, ancestors are $B, A$).

Descendant

The nodes that follow a specific node in a branch (e.g., for node $A$, descendants include $B$).

Binary Tree

A type of tree where each node has a range of $(0, 1, 2)$ children, typically distinguished as the left child and right child.

$$|A|$$

The determinant of matrix $A$, which is calculated as $257$ in the provided matrix inversion example.

$$\text{Adj } A$$

The adjoint (or adjugate) matrix, used in the calculation of an inverse matrix.

$$A^{-1}$$

The inverse of matrix $A$, defined by the formula $A^{-1} = \frac{1}{|A|} \text{Adj } A$.

$$A \times A^{-1} = I$$

The property stating that a matrix multiplied by its inverse results in the identity matrix $I$.