Advanced Topics
Advanced topics in mathematics extend beyond the standard high school and introductory college curriculum. This section covers linear algebra, discrete mathematics, number theory, and other specialized areas that are important for STEM fields.
Key Concepts
The inverse of a matrix is a square matrix $A^{-1}$ that, when multiplied by the original matrix $A$, produces the id...
The inverse of a matrix is a square matrix $A^{-1}$ that, when multiplied by the original matrix $A$, produces the id...
The inverse of a matrix is a square matrix $A^{-1}$ that, when multiplied by the original matrix $A$, produces the id...
Linear programming is a method for finding the maximum or minimum value of a linear objective function, subject to a ...
The adjugate of a matrix is the transpose of its cofactor matrix. It is a key tool for computing the inverse of a mat...
The classical adjoint (also called the adjugate) of a square matrix is the transpose of its cofactor matrix. It is co...
The classical adjoint (also called the adjugate) of a square matrix is the transpose of its cofactor matrix. It is co...
A Boundary Value Problem (BVP) is a differential equation paired with conditions that specify the values of the unkno...
Reduced row-echelon form (RREF) of a matrix is a standardized matrix form in which each leading entry in a row is 1, ...
An augmented matrix is a compact way to represent a linear system of equations by combining the coefficient matrix wi...
A linear system of equations is a collection of two or more linear equations involving the same set of variables. Eve...
A linear system of equations is a collection of two or more linear equations involving the same set of variables. Eve...
All Advanced Topics Terms (106)
- Additive Inverse of a Matrix
- Adjoint, Classical
- Adjugate
- Affine Transformation
- Aleph Null
- Algebraic Numbers
- Algorithm
- Augmented Matrix
- Boundary Value Problem
- Cardinality
- Coefficient Matrix
- Cofactor Matrix
- Column of a Matrix
- Countable
- Countably Infinite
- Curly d
- Del Operator
- Diagonal Matrix
- Dimensions of a Matrix
- Element of a Matrix
- Ellipsoid
- Elliptic Geometry
- Equivalence Relation
- Finite
- Fractal
- Gaussian Integer
- GLB
- Golden Mean
- Googol
- Googolplex
- Homogeneous System of Equations
- Hyperbolic Geometry
- Hyperbolic Trig
- Identity Function
- Identity Matrix
- Induction
- Infinite
- Infinitesimal
- Infinity
- Initial Value Problem
- Inner Product
- Invariant
- Inverse of a Matrix
- Invertible Matrix
- Kappa (Κ κ)
- Least Upper Bound
- Linear
- Linear Combination
- Linear Equation
- Linear Programming
- Linear Regression
- Linear System of Equations
- Maclaurin Series
- Magnitude of a Vector
- Main Diagonal of a Matrix
- Matrix
- Matrix Addition
- Matrix Multiplication
- Matrix Subtraction
- Möbius Strip
- Modular Arithmetic
- Modular Equivalence
- Modular Equivalence Rules
- Modular Numbers
- Multivariable
- Multivariable Analysis
- n Dimensions
- n-tuple
- Non-Euclidean Geometry
- Noninvertible Matrix
- Normal
- Normalizing a Vector
- Oblate Spheroid
- One Dimension
- Ordinal Numbers
- Ordinary Differential Equation
- Partial Derivative
- Partial Differential Equation
- Partition of a Positive Integer
- Partition of a Set
- Prolate Spheroid
- Reduced Row-Echelon Form of a Matrix
- Regression Line
- RMS
- Row of a Matrix
- Row Operations
- Row Reduction
- Second Order Differential Equation
- Self-Similarity
- Simple Closed Curve
- Skew Lines
- Spherical Trigonometry
- Spheroid
- Square Matrix
- Tautochrone
- Tessellate
- Torus
- Transcendental Numbers
- Transpose of a Matrix
- Triple (Scalar) Product
- Uncountable
- Unit Vector
- Vector
- Zero Dimensions
- Zero Matrix
- Zero Vector