### Canonical Form and Jordan Blocks

We discuss Jordan bases and the fact that an operator can be put into Jordan canonical form if its characteristic and minimal polynomials factor into

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### Canonical Form and Jordan Blocks

Read More » ### Green’s Theorem

Read More » ### Probability Density Functions (Applications of Integrals)

Read More » ### Invariant Subspaces and Generalized Eigenvectors

Read More » ### Conservative Vector Fields and Independence of Path

Read More » ### Diagonalization of a Matrix (with Examples)

Read More » ### Line Integrals

Read More » ### Finding Eigenvalues and Eigenvectors

Read More » ### Divergence and Curl of a Vector Field

Read More » ### Determinant of a Matrix (Theory and Examples)

Read More » ### Vector Fields and Gradient Fields

Read More » ### Inner Products and Orthonormal Bases

Read More » #### Feautures

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Formal Sciences

We discuss Jordan bases and the fact that an operator can be put into Jordan canonical form if its characteristic and minimal polynomials factor into

January 26, 2019 No Comments

Formal Sciences

Green’s Theorem for Simple Connected Regions Theorem. (Green’s Theorem) Let $R$ be a simply connected region with a piecewise smooth boundary curve $C$ oriented counterclockwise

January 26, 2019 1 Comment

Formal Sciences

Applications of Integrals We will consider the following applications: average value of a function over a region, mass of a lamina, electric charge, moments and

January 26, 2019 No Comments

Formal Sciences

We let $V$ and $W$ denote real or complex vector spaces. Suppose $T \in \mathcal{L}(V)$ and $U$ a subspace of $V$, then we say $U$

January 25, 2019 No Comments

Formal Sciences

Independence of Path Definition. The line integral is called independent of path if in a region $D$, if for any two points $P$ and $Q$

January 25, 2019 No Comments

Formal Sciences

An $n\times n$ matrix $A$ is called diagonalizable if $A$ is similar to some diagonal matrix $D.$ If the matrix of a linear transformation $T$

January 24, 2019 No Comments

Formal Sciences

Definition of a Line Integral Let $C$ be a smooth curve, with parametric equations $x=x(t),$ $y=y(t),$ and $z=z(t)$ for $a\leq t\leq b,$ that lies within

January 24, 2019 No Comments

Formal Sciences

Eigenvalues and Eigenvectors Let $\mathbb{F}$ be either the real numbers or the complex numbers. A nonzero vector $v$ in $\mathbb{F}^n$ is called an eigenvector of

January 23, 2019 No Comments

Formal Sciences

The Divergence and Curl Definition. Let $\mathbf{V}$ be a given vector field. The divergence of $\mathbf{V}$ is defined by div $\mathbf{V}=\nabla \cdot \mathbf{V}$ and the

January 23, 2019 No Comments

Formal Sciences

Determinants and Trace The determinant function can be defined by essentially two different methods. The advantage of the first definition, one which uses permutations, is

January 22, 2019 No Comments

Formal Sciences

Introduction to Vector Fields Definition. A vector field in $\mathbb{R}^n$ is a function $\mathbf{V}$ that assigns a vector from each point in its domain. A

January 22, 2019 No Comments

Formal Sciences

Recall that the norm of $x\in \mathbb{R}^n$ defined by $\left|\left |x\right|\right | = \sqrt{x_1^2+x_2^2}$ is not linear. To injective linearity into the discussion we introduce

January 21, 2019 No Comments

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