# Symbolic Vectors, Matrices and Arrays

By using a symbol to represent a vector, matrix or array, one gets an efficient notation to model a mathematical problem. Indeed, most scientific, engineering and statistical domains have transitioned to use this type of more abstract and efficient notation.  The Wolfram Language has a rich symbolic array language to describe problems. Most high-level solvers support symbolic array expressions and array variables, making it easy and efficient to specify high-dimensional problems.

### Symbolic Array Variables

xVectors[] assume x is a vector

xregion assume x is a vector from a geometric region

VectorSymbol define a vector symbol that can be used together with listable functions

### Symbolic Array Constants

Common zero-one arrays in array formulas.

### Symbolic Array Functions

Dot vector and matrix inner product

ArrayDot generalized array inner product

Matrix functions

Statistics functions

### Symbolic Array Predicates

Array equations and inequations

Array inequalities

### Array Derivatives

D symbolic differentiation w.r.t. vector, matrix and array variables

### Array Algebraic Equation Solvers

Solve solve equations and inequalities with array variables

### Array Optimization Solvers

Minimize optimize objectives over equality and inequality constraints with array variables

Convex optimization constraints are often expressed using vector and matrix inequalities.

### Array Integration Solvers

Integrate, NIntegrate integrate expressions with vector variables

### Array Differential Equation Solvers

NDSolve solve differential equations with array-dependent and vector-independent variables