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More determinant depth : Upper Triangular Determinant

By: Sal Khan

The determinant of an upper triangular matrix

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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More determinant depth : Determinant as Scaling Factor

By: Sal Khan

Viewing the determinant of the transformation matrix as a scaling factor of regions

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Transpose of a matrix : Rank(A) = Rank(transpose of A)

By: Sal Khan

Rank(A) = Rank(transpose of A)

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Inverse functions and transformations : Proof: Invertibility impli...

By: Sal Khan

Proof: Invertibility implies a unique solution to f(x)=y for all y in co-domain of f.

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Transpose of a matrix : Transpose of a Vector

By: Sal Khan

Transpose of a column vector. Matrix-matrix products using vectors

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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More determinant depth : Determinant when row is added

By: Sal Khan

The determinant when one matrix has a row that is the sum of the rows of other matrices (and every other term is identical in the 3 matrices)

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Transpose of a matrix : Rowspace and Left Nullspace

By: Sal Khan

Rowspace and Left Nullspace

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Functions and linear transformations : Matrix Vector Products as L...

By: Sal Khan

Matrix Vector Products as Linear Transformations

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Finding inverses and determinants : Determinants along other rows/cols

By: Sal Khan

Finding the determinant by going along other rows or columns

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Transformations and matrix multiplication : Compositions of Linear...

By: Sal Khan

Introduction to compositions of Linear Transformations

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Transformations and matrix multiplication : Distributive Property ...

By: Sal Khan

Showing that matrix products exhibit the distributive property

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Inverse functions and transformations : Relating invertibility to ...

By: Sal Khan

Relating invertibility to being onto (surjective) and one-to-one (injective)

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Finding inverses and determinants : Deriving a method for determin...

By: Sal Khan

Determining a method for constructing inverse transformation matrices

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Transpose of a matrix : Transposes of sums and inverses

By: Sal Khan

Transposes of sums and inverses

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Linear transformation examples : Introduction to Projections

By: Sal Khan

Determining the projection of a vector on s line

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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More determinant depth : Determinant after row operations

By: Sal Khan

What happens to the determinant when we perform a row operation

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Transpose of a matrix : Transpose of a Matrix Product

By: Sal Khan

Taking the transpose of the product of two matrices

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Functions and linear transformations : More on Matrix Addition and...

By: Sal Khan

More on Matrix Addition and Scalar Multiplication

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Transpose of a matrix : Determinant of Transpose

By: Sal Khan

Proof by induction that transposing a matrix does not change its determinant

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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Finding inverses and determinants : Formula for 2x2 inverse

By: Sal Khan

Figuring out the formula for a 2x2 matrix. Defining the determinant.

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.

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