Linear Algebra - Khan Academy
Khan Academy offers comprehensive linear algebra lessons, covering topics like vectors, matrices, and transformations.
Adding & subtracting matrices - Khan Academy
A matrix is a rectangular arrangement of numbers into rows and columns. Each number in a matrix is referred to as a matrix element or entry . 3 columns 2 rows ↓ ↓ ↓ → → [ − 2 5 5 2 6 7 ]
Rule of Sarrus of determinants (video) | Khan Academy
Since we solve for the determinate of a 4x4 matrix by essentially breaking it down into smaller 3x3 matrices, can we apply the Rule of Sarrus after manipulating a 4x4 into a sequence of 3x3 matrices?
Transpose of a matrix product (video) - Khan Academy
2) In quantum physics, we use matrices and other linear algebra objects and their compositions quite regularly. We also take their transpose fairly frequently (specifically, we take the Hermitian conjugate, which combines transpose and complex conjugate).
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Least squares approximation (video) - Khan Academy
That's obviously a many-to-one operation, with no unambiguous way to reverse; information is lost. The "trick" here is to squash the vector on the right-hand side of the equation down to the same smaller subspace spanned by matrix A, and then …
New category of exercises: Linear Algebra! - Khan Academy Blog
2012年10月25日 · Software developer Stephanie Chang has just launched the very first Khan Academy exercises in Linear Algebra, the college-level topic involving vectors and matrices: Matrix dimensions; Matrix addition and subtraction; Scalar matrix multiplication; Defined and undefined matrix operations; Multiplying a matrix by a vector; Multiplying a matrix by ...
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Khan Academy offers comprehensive lessons on vectors and spaces in linear algebra.
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Linear algebra. Course: Linear algebra > Unit 2. Lesson 1: Functions and linear transformations. A more formal understanding of functions ... transformations. Matrix from visual representation of transformation. Matrix vector products as linear transformations. Linear transformations as matrix vector products. Image of a subset under a ...
Orthogonal complements (video) - Khan Academy
Well, if you're orthogonal to all of these members, all of these rows in your matrix, you're also orthogonal to any linear combination of them. You can imagine, let's say that we have some vector that is a linear combination of these guys right here.