Numbers, terms, and vectors can be in arrays {matrix, mathematics}. Two-dimensional matrices have vertical positions {column, matrix}, horizontal positions {row, matrix}, and elements {cell, matrix}. Infinite matrices can have any number of dimensions, with any number of elements, as in quantum mechanics.
notation
Matrix notation is braces.
examples
One-element matrix is scalar. One-row matrix is vector.
multiplication
Matrices have products of scalars, vectors, and matrices.
purposes
Matrix elements can represent relations between set members. Matrices can be truth-tables, with element T or F listed for statement pairs. Propositions can be matrices in Boolean algebra form.
Matrices can be ordered-set components. Sequences can be n-dimensional matrices.
Matrices can represent states and operations of mathematical groups, state spaces, and symmetries. Matrices can represent particle-pair spin states.
Matrices can represent graphs. Rows and columns represent nodes. Elements are connection values between nodes.
Matrices model linear equations. Quadratic expressions use matrices to find moments of inertia. Product of solution-matrix transpose and coefficient matrix and solution matrix can find linear-equation solutions.
Mathematical Sciences>Algebra>Equation>System>Matrix
3-Algebra-Equation-System-Matrix
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Date Modified: 2022.0224