Linear Algebra 14TBD: Overview of the Properties of the Determinant

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This whole playlist, but in particular this video's explanatory style is incredible. I struggle with visual transformations so I really like seeing the "non-visual" approach. (And how it ties in to the visual)

boutiquemaths

Well done Pavel, beautifully presented.

OtterMorrisDance

The dot notation used in the upper left, | • a • b • | ... feels unfamiliar to me. I'm ~150 videos in but don't recall it, is there a name for this syntax thag I can look up elsewhere?

DanBrickley

Its so sad that the determinate is ever introduced without referencing the exterior algebra.

jak

excellent connections among properties of determinants! *0*

aglaiawong

How can we apply the fourth property of the bracket on the left: |a+b| = |a| + |b| ?
We can only use the determinant with squared matrices, hence a and b need to be squared matrices. Does this property mean that the determinant of two matrices added together equals the sum of their respective determinant?

If my statement is true, why taking the sum of two 3x3 identity matrice give us the result det(I+I) = det(I) + det(I) = 1 + 1 = 2 although by doing it on paper det(I+I) = 8 (or 2^n for any nxn identity matrice in respect to the third property of the bracket).

Could you please explain to me how to use this property as it is one of the two requirements of linearity.

Thank you.

swalscha

I can't confirm that the equality you show at 15.58 is true.
{{1, 2}, {3, 4}}+2{{1}, {3}}={{3, 4}, {9, 10}} doesn't work since determinant of {{3, 4}, {9, 10}} is not equal to determinant of {{1, 2}, {3, 4}}.
Can you please correct it for me?

matthiasandersen

good video, but I think it would of been better to break it into two or three separate ones.

terryphi

is there something called as matrix addition/subtraction? why is it not as interesting to discuss?

billchang

Linear Algebra 14TBD: Overview of the Properties of the Determinant

Linear Algebra 14TBD: Overview of the Properties of the Determinant

Linear Algebra 14TBD: The Linear Property of the Determinant

Linear Algebra 14TBD: Setting the Stage for the NxN Determinant

Linear Algebra 14TBD: The Alternating Property of the Determinant

Linear Algebra 14TBD: Interesting 2x2 Determinant Examples

Linear Algebra 14TBD: An Elegant Approach to Defining the Determinant

Linear Algebra 14TBD: An Application of the Product Property of the Determinant

Linear Algebra 14TBD: Calculating the 3x3 Determinant the American Way

Linear Algebra 14TBD: The Direct Algebraic Definition of the Determinant

Linear Algebra 14TBD: The Effect of Adding a Multiple of One Row to Another on the Determinant

Linear Algebra 14TBD: Three Ways of Calculating the 3x3 Determinant

Linear Algebra 14TBD: The Transpose Property of the Determinant

Linear Algebra 14TBD: Derivation of the 2x2 Determinant

Linear Algebra 14TBD: Area of a Triangle as a Function of Its Cartesian Coordinates

Linear Algebra 14TBD: Calculation of Areas and Volumes by the Determinant

Linear Algebra 14TBD: The Product Property of the Determinant - Proof for Elementary Matrices

Linear Algebra 14TBD: The 3x3 Determinant - A 2nd Illustration

Linear Algebra 14TBD: The Determinant is Zero ⇔ Matrix Is Singular

Linear Algebra 14TBD: The Determinant of a Triangular Matrix

Linear Algebra 14TBD: Derivation of the 3x3 Determinant

Linear Algebra 14TBD: Calculating the 3x3 Determinant the Indian Way

Linear Algebra 14TBD: Complete Proof of the Product Property of the Determinant

Linear Algebra 14TBD: Calculation of the Determinant by Gaussian Elimination

57 Introduction to determinants #math #linear #algebra