📖 Primitive Root of Unity An $n$th root of unity is a number $\\alpha$ satisfying $\\alpha^n = 1$. It is primitive if no smaller positive power of $\\alpha$ equals 1. For $n = 3$, the primitive cube roots of unity are $\\alpha = (-1 \\pm \\sqrt{-3})/2$. From: gal-edwards Learn more:

Magic Internet Math

Interactive courses covering the mathematics that powers modern technology, from foundational algebra to the cryptography securing the internet.

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Magic Internet Math

Interactive courses covering the mathematics that powers modern technology, from foundational algebra to the cryptography securing the internet.

📖 Algebraic Element An element $\\alpha \\in E$ is algebraic over $K$ if there exists a nonzero polynomial $f(x) \\in K[x]$ with $f(\\alpha) = 0$. Otherwise $\\alpha$ is transcendental over $K$. From: gal-jacobson Learn more:

Magic Internet Math

Interactive courses covering the mathematics that powers modern technology, from foundational algebra to the cryptography securing the internet.

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Magic Internet Math

Interactive courses covering the mathematics that powers modern technology, from foundational algebra to the cryptography securing the internet.

🎮 Interactive: Eigenvalue Explorer Find vectors that only get scaled by a matrix. Eigenvalues reveal the fundamental structure of linear transformations. From: Linear Algebra Try it:

Introduction to Linear Algebra | Math Academy

Interactive course based on Gilbert Strang

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Interactive courses covering the mathematics that powers modern technology, from foundational algebra to the cryptography securing the internet.

📖 Real Closed Field A field $R$ is real closed if it is ordered and has no proper algebraic extension that can be ordered. Equivalently, $R$ is real closed iff $R(\\sqrt{-1})$ is algebraically closed. From: gal-jacobson Learn more:

Magic Internet Math

Interactive courses covering the mathematics that powers modern technology, from foundational algebra to the cryptography securing the internet.

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Magic Internet Math

Interactive courses covering the mathematics that powers modern technology, from foundational algebra to the cryptography securing the internet.

📖 Left Vector Space An additive abelian group $V$ over a field $F$ with scalar multiplication $aA$ satisfying: (1) $a(A+B) = aA + aB$, (2) $(a+b)A = aA + bA$, (3) $a(bA) = (ab)A$, (4) $1A = A$. From: gal-artin Learn more:

Magic Internet Math

Interactive courses covering the mathematics that powers modern technology, from foundational algebra to the cryptography securing the internet.

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Magic Internet Math

Interactive courses covering the mathematics that powers modern technology, from foundational algebra to the cryptography securing the internet.