Question about the determinant of an upper triangular matrix Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Getting the determinant value of the original matrix from its upper triangular matrixHow is diagonal matrices a subspace of upper triangular matrices?Upper Triangular Matrix DefinitionTransforming a matrix to upper triangular formWhat is the transformation matrix “by definition”?How to derive the Vandermonde Determinant?Various matrix manipulations effect on determinantDeterminant of Partitioned Upper Triangular MatrixHow would I answer the following question about the determinant of a matrix?Determinant of Triangular Matrix
Can gravitational waves pass through a black hole?
How can I prevent/balance waiting and turtling as a response to cooldown mechanics
What does 丫 mean? 丫是什么意思？
Did any compiler fully use 80-bit floating point?
Why do the Z-fighters hide their power?
Should man-made satellites feature an intelligent inverted "cow catcher"?
Does the universe have a fixed centre of mass?
.bashrc alias for a command with fixed second parameter
What should one know about term logic before studying propositional and predicate logic?
Fit odd number of triplets in a measure?
How to make an animal which can only breed for a certain number of generations?
How do you cope with tons of web fonts when copying and pasting from web pages?
Getting representations of the Lie group out of representations of its Lie algebra
Where did Ptolemy compare the Earth to the distance of fixed stars?
The test team as an enemy of development? And how can this be avoided?
One-one communication
How to resize main filesystem
Searching extreme points of polyhedron
First paper to introduce the "principal-agent problem"
Is there night in Alpha Complex?
How to name indistinguishable henchmen in a screenplay?
Noise in Eigenvalues plot
Why does BitLocker not use RSA?
why doesn't university give past final exams' answers
Question about the determinant of an upper triangular matrix
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Getting the determinant value of the original matrix from its upper triangular matrixHow is diagonal matrices a subspace of upper triangular matrices?Upper Triangular Matrix DefinitionTransforming a matrix to upper triangular formWhat is the transformation matrix “by definition”?How to derive the Vandermonde Determinant?Various matrix manipulations effect on determinantDeterminant of Partitioned Upper Triangular MatrixHow would I answer the following question about the determinant of a matrix?Determinant of Triangular Matrix
$begingroup$
I was watching an online lecture on the properties of determinants and at 27:00 in this lecture: https://www.youtube.com/watch?v=srxexLishgY&t=4s, the professor did a step which I don't understand.
If $A = beginpmatrixd1 & 0 & 0\ 0 & d2 & 0\ 0 & 0 & d3endpmatrix $, then according to the lecturer, $A=d1 *d2 *d3 beginpmatrix1 & 0 & 0\ 0 & 1 & 0\ 0 & 0 & 1endpmatrix$, this was then used to show that the determinant of an upper triangular matrix can be written as the product of the leading diagonal
. However I thought if a matrix is multiplied by a number, all elements of the matrix are multiplied by it. Is this just wrong?
linear-algebra matrices determinant
asked Apr 2 at 16:37
Vishal JainVishal Jain
62
$endgroup$
add a comment |
$begingroup$
I was watching an online lecture on the properties of determinants and at 27:00 in this lecture: https://www.youtube.com/watch?v=srxexLishgY&t=4s, the professor did a step which I don't understand.
If $A = beginpmatrixd1 & 0 & 0\ 0 & d2 & 0\ 0 & 0 & d3endpmatrix $, then according to the lecturer, $A=d1 *d2 *d3 beginpmatrix1 & 0 & 0\ 0 & 1 & 0\ 0 & 0 & 1endpmatrix$, this was then used to show that the determinant of an upper triangular matrix can be written as the product of the leading diagonal
. However I thought if a matrix is multiplied by a number, all elements of the matrix are multiplied by it. Is this just wrong?
linear-algebra matrices determinant
asked Apr 2 at 16:37
Vishal JainVishal Jain
62
$endgroup$
add a comment |
$begingroup$
I was watching an online lecture on the properties of determinants and at 27:00 in this lecture: https://www.youtube.com/watch?v=srxexLishgY&t=4s, the professor did a step which I don't understand.
If $A = beginpmatrixd1 & 0 & 0\ 0 & d2 & 0\ 0 & 0 & d3endpmatrix $, then according to the lecturer, $A=d1 *d2 *d3 beginpmatrix1 & 0 & 0\ 0 & 1 & 0\ 0 & 0 & 1endpmatrix$, this was then used to show that the determinant of an upper triangular matrix can be written as the product of the leading diagonal
. However I thought if a matrix is multiplied by a number, all elements of the matrix are multiplied by it. Is this just wrong?
linear-algebra matrices determinant
asked Apr 2 at 16:37
Vishal JainVishal Jain
62
$endgroup$
I was watching an online lecture on the properties of determinants and at 27:00 in this lecture: https://www.youtube.com/watch?v=srxexLishgY&t=4s, the professor did a step which I don't understand.
If $A = beginpmatrixd1 & 0 & 0\ 0 & d2 & 0\ 0 & 0 & d3endpmatrix $, then according to the lecturer, $A=d1 *d2 *d3 beginpmatrix1 & 0 & 0\ 0 & 1 & 0\ 0 & 0 & 1endpmatrix$, this was then used to show that the determinant of an upper triangular matrix can be written as the product of the leading diagonal
. However I thought if a matrix is multiplied by a number, all elements of the matrix are multiplied by it. Is this just wrong?
linear-algebra matrices determinant
linear-algebra matrices determinant
asked Apr 2 at 16:37
Vishal JainVishal Jain
62
asked Apr 2 at 16:37
Vishal JainVishal Jain
62
asked Apr 2 at 16:37
Vishal JainVishal Jain
62
asked Apr 2 at 16:37
Vishal JainVishal Jain
62
asked Apr 2 at 16:37
Vishal JainVishal Jain
62
62
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
you are right about multiplying a matrix by a constant.
The professor in the video is also right, because he is calculating the determinant of the matrix.
answered Apr 2 at 16:40
MoonKnightMoonKnight
1,673611
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3172083%2fquestion-about-the-determinant-of-an-upper-triangular-matrix%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
you are right about multiplying a matrix by a constant.
The professor in the video is also right, because he is calculating the determinant of the matrix.
answered Apr 2 at 16:40
MoonKnightMoonKnight
1,673611
$endgroup$
add a comment |
$begingroup$
you are right about multiplying a matrix by a constant.
The professor in the video is also right, because he is calculating the determinant of the matrix.
answered Apr 2 at 16:40
MoonKnightMoonKnight
1,673611
$endgroup$
add a comment |
$begingroup$
you are right about multiplying a matrix by a constant.
The professor in the video is also right, because he is calculating the determinant of the matrix.
answered Apr 2 at 16:40
MoonKnightMoonKnight
1,673611
$endgroup$
you are right about multiplying a matrix by a constant.
The professor in the video is also right, because he is calculating the determinant of the matrix.
answered Apr 2 at 16:40
MoonKnightMoonKnight
1,673611
answered Apr 2 at 16:40
MoonKnightMoonKnight
1,673611
answered Apr 2 at 16:40
MoonKnightMoonKnight
1,673611
answered Apr 2 at 16:40
MoonKnightMoonKnight
1,673611
1,673611
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3172083%2fquestion-about-the-determinant-of-an-upper-triangular-matrix%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
